No, and no.
The Pharisees clearly had not had it given to them to come to the Son:
Joh_6:37 All that the Father giveth me shall come to me; and him that cometh to me I will in no wise cast out.
"But there are some of you who do not believe." (For Jesus knew from the beginning who those were who did not believe, and who it was who would betray him.) And he said, "This is why I told you that no one can come to me unless it is granted him by the Father."
(Joh 6:64-65)
Nor is God obligated to grant grace to everyone:
"As it is written, Jacob have I loved, but Esau have I hated. What shall we say then? Is there unrighteousness with God? God forbid. For he saith to Moses, I will have mercy on whom I will have mercy, and I will have compassion on whom I will have compassion."
(Rom 9:13-15)
Nor can anyone believe unless they are of God:
Joh 8:47 He that is of God heareth God's words: ye therefore hear them not, because ye are not of God.
The Gentile world without knowledge of the true God were without hope, and utterly doomed, which was why it is necessary to preach to them. Without faith in the true God, there is only damnation:
Eph_2:12 That at that time ye were without Christ, being aliens from the commonwealth of Israel, and strangers from the covenants of promise, having no hope, and without God in the world:
Act_16:9 And a vision appeared to Paul in the night; There stood a man of Macedonia, and prayed him, saying, Come over into Macedonia, and help us.
Rom_10:17 So then faith cometh by hearing, and hearing by the word of God.
Titus 2:11 must be kept in its context and the way the Jews use language. From a previous posting:
"... One must be aware of the unique peculiarities Jews make use of in their language. For example, from Gills commentary, commenting on the Jewish use of the words all the world, the world, the whole world, all the men of the world, etc, Gill begins by quoting Jewish examples where the word is used in radically different ways from how we would use it today:
"Nothing is more common in Jewish writings than to call the Gentiles, the world; and the whole world; and the nations of the world (l); See Gill on John 12:19; and the word world is so used in Scripture; see Joh_3:16; and stands opposed to a notion the Jews have of the Gentiles, that there is no propitiation for them (m): and it is easy to observe, that when this phrase is not used of the Gentiles, it is to be understood in a limited and restrained sense; as when they say (n),
it happened to a certain high priest, that when he went out of the sanctuary, the whole world went after him;(n)
which could only design the people in the temple. And elsewhere (o) it is said,
amle ylwk, the whole world has left the Misna, and gone after the Gemara;
which at most can only intend the Jews; and indeed only a majority of their doctors, who were conversant with these writings: and in another place (p),
amle ylwk, the whole world fell on their faces, but Raf did not fall on his face;
where it means no more than the congregation. Once more, it is said (q),
when R. Simeon ben Gamaliel entered (the synagogue), the whole world stood up before him;
that is, the people in the synagogue: to which may be added (r), when a great man makes a mourning, the whole world come to honour him; i.e. a great number of persons attend the funeral pomp: and so these phrases, the whole world is not divided, or does not dissent (s); the whole world are of opinion (t), are frequently met with in the Talmud, by which, an agreement among the Rabbins, in certain points, is designed; yea, sometimes the phrase, all the men of the world (u), only intend the inhabitants of a city where a synagogue was, and, at most, only the Jews: and so this phrase, all the world, or the whole world, in Scripture, unless when it signifies the whole universe, or the habitable earth, is always used in a limited sense, either for the Roman empire, or the churches of Christ in the world, or believers, or the present inhabitants of the world, or a part of them only, Luk_2:1; and so it is in this epistle, 1Jo_5:19; where the whole world lying in wickedness is manifestly distinguished from the saints, who are of God, and belong not to the world; and therefore cannot be understood of all the individuals in the world (From Gills Commentary on 1 John 2:2, quoting from (l) Jarchi in Isa. liii. 5. (m) T. Hieros. Nazir, fol. 57. 3. Vid. T. Bab. Succa, fol. 55. 2. (n) T. Bab. Yoma, fol. 71. 2. (o) T. Bab. Bava Metzia, fol. 33. 2. (p) T. Bab. Megilla, fol. 22. 2. (q) T. Bab. Horayot, fol. 13. 2. (r) Piske Toseph. Megilla, art. 104. (s) T. Bab. Cetubot, fol. 90. 2. & Kiddushin, fol. 47. 2. & 49. 1. & 65. 2. & Gittin, fol. 8. 1. & 60. 2. (t) T. Bab. Kiddushin, fol. 48. 1. (u) Maimon. Hilch. Tephilla, c. 11. sect. 16.)
Scriptural examples of this include:
Luk 2:1 In those days a decree went out from Caesar Augustus that all the world should be registered.
By this Luke means, not the whole habitable world, as much of it was still undiscovered, and not even the whole known world, which even in those days was not all under the power of the Roman empire, but just the Roman empire itself, or perhaps Judae. Another one, which Gill mentioned:
1Jn 5:19 We know that we are from God, and the whole world lies in the power of the evil one.
Obviously we are no longer under the power of Satan, but have been released from his clutches by the power of Jesus Christ. Another:
Luk 11:42 But woe to you Pharisees! For you tithe mint and rue and every herb, and neglect justice and the love of God.
These you ought to have done, without neglecting the others. Some translations render this all manner of herb, but, literally, it is every herb, which, obviously, the meaning is only every kind of herb.
Another example:
As it is written, There is none righteous, no, not one: There is none that understandeth, there is none that seeketh after God. (Rom 3:10-11)
Obviously this cannot mean that no one seeks or understands, as all Christians seek and understand (though maybe not perfectly). But, Pauls meaning is more general, referring to the depraved world, or of all Christians prior to Christ saving them, who, before that time, are incapable of seeing, believing or understanding until the Holy Spirit moves on them. Another example, Christ distinguishing between the world and those given to Him out of the world:
Joh 17:9 I pray for them: I pray not for the world, but for them which thou hast given me; for they are thine.
Thus the world does not mean everyone in the world, but all those not given to Him.
Another example:
Joh_12:19 The Pharisees therefore said among themselves, Perceive ye how ye prevail nothing? behold, the world is gone after him.
Obviously the whole world wasn't going after him, and so the Pharisees here only speak of the "world" in the same sense they do all over their Talmud. Finally, more direct examples, by comparing seemingly contradictory verses with their parallels:
1Jn_2:2 And he is the propitiation for our sins: and not for ours only, but also for the sins of the whole world.
Joh_11:52 And not for that nation only, but that also he should gather together in one the children of God that were scattered abroad.
Thus the meaning is, Christ is the atonement for all the sins of the children of God scattered abroad, of every nation and tribe.
As for John 1:9-- Christ is the light of the whole world, but there are various degrees and meanings of "light." Clearly the whole world did not receive the light of faith, since it is said that no one "seeks after God, no one understands God." Again, the Pharisees were not given by the Father to the Son to come to Him, but disbelieved Him because it was not given to them to believe. But all men receive the law of God imprinted on their hearts which condemns them and leaves them without excuse, and all men owe their existence to God, who grants life to all men, even though they-- on a spiritual level-- are full of darkness and are unwilling to believe.