Can a man be saved without them? Let me be very clear here, because I know the tendency is to try to distort what Calvinists say. The man performs the acts. I don't think there can be any argument on that point. The question is, does he perform the acts totally on his own initiative, or does God enable the man to do so?
The Arminian says that salvation is of God.
The Calvinist says the same.
The Arminian says that the man must choose to come to God, but they don't address his ability to do so. The assumption is that man is able to make that choice, unaided, only needing to hear the Gospel.
The Calvinist says that man cannot choose to do so on his own, so God must first enable the man to hear the Gospel so that he CAN believe it, and receive Christ.
The Arminian says that's "Prevenient Grace", that wonderful catch-all term that is at the same time universal, yet specific, and sufficient by itself to enable man to make his own choice to receive Christ.
The Calvinist says that God's enabling of the man is Irresistable Grace, or Effectual Grace, meaning that it is specific, not universal, and that it is never failing in those to whom it is granted.
The Arminian says that God does not override man's free will in this, that the man's free will is sacrosanct, inviolable, or God would be some sort of draconian monster, pushing people around, and making them do things they don't want to do, although they never really explain why God forcing someone to be saved would be a bad thing, seeing that it is of infinite value to the one so saved.
The Calvinist says that God, without consulting the man's will, unilaterally resuscitates the sinner's dead, cold, stony heart of sin, a heart that is incapable of hearing or believing the gospel (the preaching of the gospel is to them that perish foolishness), thereby enabling the man to hear the Gospel with spiritually-alive ears so that Faith can come (faith cometh by hearing, and hearing by the Word of God), and the man can believe, the Gospel, receive forgiveness of sins, Christ can dwell in his heart (which must be spiritually alive), and he can receive justification.
The man is the one doing the believing and receiving, God is the one that makes it possible. Man freely chooses to do so, because he has been made spiritually alive by the power and Grace of God, but he cannot do those things UNTIL he is FIRST made spiritually alive. Spiritually-dead men cannot believe savingly, cannot receive Christ into their hearts, and cannot be justified, because they are spiritually dead. No spiritually-dead man can ever do any act pleasing to God. Only spiritually-alive men can do so.
Can a man be saved without them?
It would appear that would be the case.
I say that because it is my understanding that for God to bring a man to perform a God-pleasing act then he is predestined for salvation. He is already saved no act is required or necessary or this would deny God's sovereignty.
If this is not the case than the works of man in some manner are required for salvation?