What would actually happen if Alabama unilaterally decided to not issue/recognize gay marriages?
It would be pretty hard to get every county to stop issuing licenses, but if it did happen, it would be a huge mess. You could try to get the district court judge for the state to issue a fresh ruling, but that wouldn't be a guaranteed solution because Moore says only the AL Supreme Court can require SSM, which is run by him and therefore will never issue a favorable ruling on the issue or (likely) even hear such a case. You could look at trying to jail probate judges, but that might not even be possible because AL marriage laws use the word 'may' instead of 'shall' when giving probate judges the power to issue marriage licenses. The 9th circuit and the US supreme court could issue new rulings just for AL in an attempt to make Moore rescind his order, but there's no guarantee Moore would even listen to either of them, since they would likely be tied to grievances of a certain set of specific couples, allowing Moore to use effectively the same argument he's making now to keep his order in effect.
Of course, the nuclear option is for Obama to send in the national guard to force compliance. I'm not sure if Obama is bold enough to do that though.