As someone points out in the book itself (though I don't remember where now), it's likely that other Amyrlins were elected by Black Ajah Sitters - indeed, Egwene was. They try to make an argument that it's different because Egwene had enough votes to make it even without the Black votes, but I can't see how that makes any legal difference, to be honest. Political, yes. Legal, no. Trying to declare binding votes invalid retroactively because you realize afterwards that some of the voters were criminals doesn't make much sense, and is an enormous slippery slope besides - a number of other decisions of both the Tar Valon Hall and the Salidar one might suddenly prove invalid as well if you follow that line of argument, including, ironically, Salidar's decision to go to war on Tar Valon all the way back in tPoD. Take out Delana's and Moria's votes in favour, and the decision fails to pass, I just checked. See link.

So honestly, Elaida's election was legal, that wasn't the problem with it. If anything strictly speaking illegal happened during that coup, it's more likely to have been the murder of Alric or other things.