@oralloy,
Generally speaking, yes. Unless that that state law violates the Constitution as when the SCOTUS struck down capital punishment laws in various states. Or ruled that redistricting was gerrymandering in various states.
A state can write laws that meet or exceed the limits of Federal law if that new law does not specifically break Federal law and (that's what Federal and District courts are about) and if that new law is Constitutional.
A state can't make slavery legal. Deny the vote to any segment of the population like white males, legalize murder for example.
So, yeah a state can try to ban abortion, but so far the Supreme Court has thrown any outright bans out, and so far has ruled that most of the restraining sorts of regulations do not not pass Constitutional muster.