There is of course no precise link between popularity and playability, but I think it does play a role. I doubt that Kokonoe would have ever become playable for example if fans hadn't been asking for it for years. Fanart isn't an exact metric, but it is suggestive. In this popularity contest, made a few months after the start of the manga, Mai didn't even make the list. I doubt she did much better in the more recent ArcSys popularity contest, though I would be interested in hearing her exact ranking if someone knows it.
Of course preexisting popularity isn't a requirement for playability; after all if that were the case no new characters would be created since they have no established fans. But if an existing character seems unpopular, the game developers might decide that adding a completely new character instead would do a better job of attracting buyers.