No, under Reformed theology all men are called to repentance. Westminster Confession-Chapter XV Of Repentance unto Life . Even after becoming Christians we are to continue to repent for our sins.
The issue that is really puzzling you is why would God require man to repent unless He gave man the ability to repent? Frankly, I don't know. It simply the way it is. The nature of God can be succinctly wrapped up in Augustine's prayer, "Command what you will, and grant what you command." God commands all men to repent, and He must grant us the ability to repent. God commands us to love one another, yet God must give us the ability to love. God commands us to be fruitful and yet it is God who produces the fruit. All of scripture is filled with these differing verses.
Augustine's prayer was right, God commands us and then He also grants (or not) the ability to carry it out. This is the very nature of God. I will say that this idea seem so preposterous to Pelagius that he found offense with this prayer. The church sided with Augustine and the clear teaching of scripture. Augustine and Pelagius
1. What is the purpose for the non-elect to repent? What happens if they do? What happens if they don’t.
2. What is the purpose for the elect to repent? Is it strictly a mechanical act? It would seem so.
“The issue that is really puzzling you is why would God require man to repent unless He gave man the ability to repent? Frankly, I don’t know. It simply the way it is. “
No it isn’t. The issue that is puzzling me is why would all men be commanded to repent if the elect have been selected before they were born and the non elect are going to hell. Are there different temperatures of hellfire in Reformed theology? Does a repentent non-elect get the occasional beer?
Another issue that is puzzling me is why would the elect be commanded to repent if they are going to heaven anyway. A couple of you guys have voiced some weak and incomplete thoughts about temporal punishment or even levels of reward in Heaven - I see where Joseph Smith was influenced in his theology here - but I can see nothing that stands on its own and certainly nothing Scriptural.
You see why we think of Calvinism as illogical and evil in itself?