I'd say that at this point you'd be better off turning it into a normal PS3 and then installing a custom firmware. There's a lot of great homebrew for it, it makes for a great emulation machine, and it's still the best non-UHD bluray player on the market. Also, if you have a model that natively supported linux, then it is also likely to be a model that had PS2 backwards compatibility. Without knowing the model I can't say for sure, but considering you'd in theory have one machine that can play almost everything from three generations of PlayStations, I think you'd be better served using it as one.
Also, while I can't say for sure, I'd imagine that software support under Linux isn't going to be that great as you'd be running most if not all software on just the Cell's single 2 thread general purpose PPE PowerPC core, with 256 MB of system memory. So, I don't see it being all that useful outside of maybe running as a server for something on your network, which frankly a raspberry pi would probably be better suited for at this point considering performance and power usage. If the Cell's 7 supplemental SPE cores aren't taken advantage of by software the performance is pretty poor.
TLDR, open the sucker up, give it a good cleaning, repaste the CPU and GPU, flash the official firmware on it, and then flash a custom firmware or PS3HEN on it and take advantage of the homebrew and emulation support. Plus, PS3 games are dirt cheap at this point. I recently got a PS3, and I picked up the Last of Us at Gamestop for 3 USD. Lots of great games on the system, and most of them are very cheap.
Getting Linux working on the early PS3s was cool.... and it could have turned into something fantastic. Buy Sony did a good job of correcting their oversights in following models meaning the initial wave of support died off. So ya if you can do it I think everyone is right make it a homebrew PS3 machine. If Sony had turned a blind eye and the community kept supporting Linux on there... I have no doubt there would be some great distros for them. Alas there isn't... nothing it can do that a 10 year old salvage part PC can't do better.