This assumes the black market cannot provide safe abortions.

Historically, no it doesn’t. Not unless you’re wealthy and can pay a real doctor enough to be willing to risk jail.

Otherwise it’s coat-hangers and the other risky improvised methods used for millennia before modern medicine.

The rich will always have whatever they want. There could be a reduction in total abortions, but there will always be direct actionists fighting for women's rights. Emma Goldman and the first wave feminists were only the beginning.