It is my non-professional opinion that this would be a risky thing to do. It might work for a time then fail or it might work just fine for years, but it's a "get by with" fix at best. it may well be the reason the toilet leaked was due to those screws allowing movement which broke the wax ring seal. I would suggest removing the flange and replacing it with one install properly would be the wise way to go. I suspect you already know this and are hoping to some suggestions for an easy fix. Perhaps the pros will have some way to repairing this without a complete flange replacement, but I doubt any of them will OK the screws into the floor.