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.
The upcoming election(on May 14th if it doesn't get postponed due to the earthquake) will be unique across other elections Erdogan participated in over the last 20 years. This was the first election he might actually lose(by a margin of 5-10%) according to election polls before the earthquake.
So he did care about his popularity as he was the most popular one so far. Voters and the system were surely manipulated by the ruling party in the decade but opposing a decisive election result is a new line they haven't crossed yet.
> Anger Over Quake Response Challenges Erdogan Ahead of Election
> A furor is building among some survivors over the government’s handling of the crisis. “I have been voting for this government for 20 years, and I’m telling everyone about my anger,” said one. “I will never forgive them.”