I have heard of precancerous cells of the cervix clearing after birth, could the same be said following an abortion?

Probably not: I'm not aware of any data shoing that cervical dysplasia (precancerous cells), or the HPV infection that causes it, clear up more rapidly after abortion than otherwise. And clearance after delivery is questionable. What probably happens is that clearance is delayed by natural immune suppression during pregnancy, and after delivery there is catch-up clearance as the immune system returns to normal.