Yes you can. i believe Yellow Dog Linux (the official linux distro for PS3) has Firefox built into it as the requisite web browser.
I've said this before ad i will again- make sure to read up a good bit about the install before doing it as well as instructions on how to switch back to normal PS3 use. Linux can be a bit tricky to work with and it isn't hard to mess something up (as i found out with my previous computer).