The Supreme Court would only take a case if the law had not been invalidated by the lower courts. And it is a virtual certainty that the Alabama law will be summarily invalidated in its entirety by the lower courts. Thus, if the Supreme Court does not take a case relating to that law, it will only be because the law is already dead in its entirety.
I predict that the Alabama law, as well as the several "heartbeat" bills, will be invalidated by the Courts of Appeal. The SCOTUS will let those decisions stand, thereby wasting all the efforts of those legislatures trying to get a test case before the Supreme Court.
These laws are simply too extreme and repugnant to liberty to be Constitutional. A better case, IMO, may be those laws that severely restrict the procedure after 20 weeks (that are, in other words, similar to abortion restrictions that exist in Europe.) Those laws, which aren't extreme and allow (IMO) a meaningful opportunity for a woman to make her choice, may be either upheld or rejected by a Court or Appeals. If there is a split in the circuits, the SCOTUS may be prompted to intervene and resolve the conflict.