No. It really doesn’t.
To see why, let’s look at a hypothetical situation. Let’s pretend that you are insanely wealthy and you decide you like me. You want to do something huge for me that will change my life. You want to elevate me to millionaire status. So you write me a check for ten million dollars.
Now in order for me to actually take possession of that money I have to do something. I have to endorse the check and deposit it in my bank account. Until I do that, it’s just a scrap of paper.
If, after depositing the check, I claimed to be a self-made man, started boasting, and got puffed up thinking how amazing I am for making myself rich because of all the work I did for that to happen, I’d be pretty silly. Even though it is true that I never would have been able to benefit from that money without depositing the check, it obviously wasn’t anything that I did that made me rich. My change is status was entirely your doing, a result of your generosity.
Salvation is the same. All the work, credit, and glory belongs to God. He hands every single person a check for their salvation. At the same time no one gets the benefit of that payment until they receive it. The choice is indeed theirs, deposit the check or don’t. God does not “make” anyone receive his salvation.