Data from other countries who have banned abortion are somewhat informative, despite those countries being mostly 3rd world backwaters.
When abortions are outlawed, the rate of abortions remains essentially unchanged. They merely occur in an unregulated environment, with a large increase in poor medical outcomes from shoddily-performed procedures, especially affecting poorer women.
Outlawing abortions to make them go away is like outlawing drugs and pretending that drug use then just goes away.
Make no mistake, almost everyone on both sides of the aisle want abortions to be rare. Removing it from the health care system seems a poor way to accomplish this, however.