Sure, yes...
Diogenes (the character) was a famous, upper class dude. Lifelong poverty wasn't a trap he couldn't escape.
Also I didn't mean to be too harsh. The "can't wait to tell you how little I care" trope is one we can't escape even in modern dissident youth culture. Hippies, punk, goth, emo... every generation reinvents it and it's artistically/culturally rich ground.
That said, the Diogenes character definitely does seem like he enjoyed being the centre of attention. It's like Marilyn Manson going on daytime talk shows in the 90s to tell normies that he doesn't care what they think. There's obviously a falsity in there, somewhere. It got my attention though, as a teen, and I still listen to th albums.
The point of the barrel is to be seen in a barrel, at the very least to demonstrate the philosophical reasoning for the barrel.
There are plenty of people who genuinely don't care what the people of Corinth think, say or do. The don't choose to spend their time in the public square debating.