Okay, seeing as Ché sings and plays some instruments, I'm obviously biased towards interesting RP.
If a Gallentean char claims to have starred in some movies or something, I might pretend I've seen some of his work. I don't know if claiming fame is god-modding, but it's a relatively innocent version if it's done well. Fame has downsides as well, after all, and some of us may be at least local celebrities for just being the capsuleer from their community. Claiming fame is in my eyes mostly just another hook for interaction with other characters, thus beneficial to RP in that aspect.
Ché's fame comes mostly from racing, but his musical interactions with other characters provide entertaining RP.