A hospital will not reject a woman who may be dying no matter the cause. I would doubt that it would even be legal.
Question: where is there any info about the Tiller Killer that may counter the claims that he was pro-life?
No they won't but the state won't give a license to an abortuary (or any other outpatient surgery center) without an agreement with a nearby hospital in case of emergency.
Of course, the woman would be admitted and/or treated by way of the Emergency Room. But, that is very different from this murderous scumbag having “admitting priveleges” in a formal kind of arrangement. I think it’s a very important distinction. With Tiller, since he already had such priveleges before he went into full-time murder-for-hire, it likely would have required a lawsuit to revoke those priveleges.
As to the info you're seeking: Google is your friend. (or try 'Bing'.)