Not at all, it implies no such thing.
It is impossible for men to repent.
No, it doesn't imply ability, John 6 and many other passages deny mans ability.
Salvation is not received or granted for doing anything as you're implying via your question. People are not saved because they did something commanded any more than they could fulfill the Law and be saved.
You're the only one bringing up a phantom false dichotomy, something that doesn't exist in our dialog.
I read Hitchhiker's Guide to the Galaxy when I was young, and there was a story in it I will retell to the best of my memory. One of the characters was the real power behind the government, as opposed to the figure-head president. He was supposed to be the smartest person in the galaxy. He would sit around wondering whether the table he was sitting at was real. A spaceship with the people who were sent to consult with him left one member behind. The man stood outside his cabin banging on the door while the smart being in the house sat there contemplating whether the sound was real or if reality was all in his imagination.
Your comments remind me of that. I think you are talking the Calvinism too far. If men cannot repent, then the 3000 on the day of Pentecost would not have repented and been baptized and were not added to the church.
I don't see the apostles engaging in this kind of psuedo-intellectual babble when they were evangelizing. If people believed and were saved, God worked in them to do that. God works in people, and people repent.