Of course. It is an error to regard our liturgical work as meriting salvation, -- that would be a form of pelagianism, -- but it is equally an error to say that divine mercy is not moved by pleas for mercy. Let us remember that we do not go to mass to get anything, but rather to simply be at the hill of Golgotha.
Does God know the names of all the elect for all time at this very minute?
Yes. I don't think we will ever be able to truly figure out the interaction between God and our cooperation - how one effects the other. After a certain point, we can only speculate. We do know that prayer is effective, and we do know that God has predestined the saved, so go figure...!
Regards