No, it doesn't.
Hebrews 7:1 says that Melchizedek was king of Salem - Jerusalem - and a priest of God. Verse 3 says that he resembles the Son of God, not that he WAS the Son of God. And the OT quote was, "you are a priest forever in the order of Melchizedek", Psalm 110:4.
I agree. Christ can simply mean anointed one. Priests, prophets and kings were anointed ones.
Abraham, Isaac, and Jacob were anointed ones as well.
1 Chron 16:15 Be ye mindful always of his covenant; the word which he commanded to a thousand generations;
16 Even of the covenant which he made with Abraham, and of his oath unto Isaac;
17 And hath confirmed the same to Jacob for a law, and to Israel for an everlasting covenant,
18 Saying, Unto thee will I give the land of Canaan, the lot of your inheritance; {the lot: Heb. the cord }
19 When ye were but few, even a few, and strangers in it. {few, even: Heb. men of number, etc }
20 And when they went from nation to nation, and from one kingdom to another people;
21 He suffered no man to do them wrong: yea, he reproved kings for their sakes,
22
Saying, Touch not mine anointed, and do my prophets no harm.
Ps 105
8 ¶ He hath remembered his covenant for ever, the word which he commanded to a thousand generations.
9 Which covenant he made with Abraham, and his oath unto Isaac;
10 And confirmed the same unto Jacob for a law, and to Israel for an everlasting covenant:
11 Saying, Unto thee will I give the land of Canaan, the lot of your inheritance: {lot: Heb. cord }
12 When they were but a few men in number; yea, very few, and strangers in it.
13 When they went from one nation to another, from one kingdom to another people;
14 He suffered no man to do them wrong: yea, he reproved kings for their sakes;
15
Saying, Touch not mine anointed, and do my prophets no harm.
16 Moreover he called for a famine upon the land: he brake the whole staff of bread.