I think it's probably relevant, yes -- he is in fact fairly popular, historically. (So is Putin). It's harder to keep your hands on the levers of power the less support you have, even if it can still be done with increasing force, it's a threat.
But I'm interested in hearing with Turkish HN users think.
Note that the comment I replied to, from a Turkish user, suggested "They are only interested in the optics and looking strong for the upcoming election", suggesting that, yes, Erdogan cares about popularity.