No, restricting access to abortion will not by itself (re)create a culture of life, but it IS part of the solution.
Law is not just shaped by culture; it is a powerful shaper of culture. Law Teaches. Never forget that.
? If we can get the Law to treat abortion as something undesirable, something fraught with unacceptable public risk, something degrading and dangerous to be firmly suppressed when possible, something profitable only to unsavory corporate creeps, something available only in a very limited number of places and times --- heck, if they would treat the abortion industry the way they treat the tobacco industry ---
It's not enough for abortion to be illegal. It should be uncool - then distasteful - then abhorrent - then unthinkable.
Those are good points, but it a chicken and egg sort of problem as I see it.
How did we get to this point where abortion is so common? The problem was culture to being with. Before abortion became relatively safe (and legal) there children being left behind [look baby farms in England] and there have always been parents who are irresponsible and a culture that did not hold people who procreate to equal standards.
This culture did not just spring up out of nothing.