Zoidar, you say, "But if an unbeliever asks: "Did Jesus die for me?" [Calvinists] can't say anything".
But they most definitely can say something. From my point of view, and, of course, depending on how much they know about God and his Gospel, the first answer is, "do you want him?".
Mike you are exactly right. The argument so many have claimed, that 'whosoever' believes, (or calls upon the name, and other phrases) rules out predestination of the elect, is not only useless, but the same fact that renders it useless also applies to the question of evangelism by those who believe in Election —"WHO is it that believes?" If God does not love everyone, (and I'm not denying that in some form God does love everyone, but that's beside the point), there is nothing to be gained by fooling all in order that the elect might believe.
I've seen much effort in sowing seed, as if it was also harvest. I've watched churches making sure of the 'most effective' use of money in Evangelism, without the slightest concept that 'most hearers' or 'most needy' does not necessarily translate to most converts, and 'most converts' doesn't translate to most Redeemed. I thank God for the 'hit and run evangelist', but man, I don't enjoy listening to their mindset.
So, to the question of whether the Reformed can evangelize effectively, without compromising their theology: Most, even Arminian, believers are otherwise adamant that the TRUTH be told, regardless of the consequences or apparent efficacy, yet somehow I keep running into this mindset that we must sell the Gospel. OF COURSE, there is a place for doing as Paul did, to be all things to all people that he might win some. Nevertheless, in Paul's evangelism I don't see ANYTHING that goes against what has become known as Calvinism or Reformed teaching, nor do I see him backing off of telling the facts. "22 “Fellow Israelites, listen to this: Jesus of Nazareth was a man accredited by God to you by miracles, wonders and signs, which God did among you through him, as you yourselves know. 23 This man was handed over to you by God’s deliberate plan and foreknowledge; and you, with the help of wicked men, put him to death by nailing him to the cross. 24 But God raised him from the dead, freeing him from the agony of death, because it was impossible for death to keep its hold on him."" (Acts 2)
It's better to say, "Listen to what God says", than to say, "God is a sweet old man who wants you so badly that he died for you, but it's up to you!"
The Word of God never returns to him void. If God uses the truth to harden someone's heart, what is the problem? I want GOD to change a heart; the intellect and emotions can't do it.
What do these who water down the Gospel say, when the agnostic says, "If God loves me, then why was I abused?"? "Well, God didn't really mean for you to be abused, but, see, we have freewill." Doesn't even sound close to, "Fear him who is able to destroy both body and soul in hell".
There is no useless evangelism, but if anything ever came close to it, it would be through the preaching of a 'winsome' gospel that ignores the truth.