Technically yes - nothing is stoping Sony to let PS3 silently "call home" even when not signed in PSN and let them know what you're up to but I doubt anything like that is actually implemented in any of the current firmwares but if you want to be on the safe safe simply prohibit your PS3 from going online - either by blocking it on your router or by setting the IP manually and removing the DNS servers and Default Gateway - although some uber paranoic users believe PS3 could be looking for the fixed IPs rather than just URLs. Then indeed you'd need to isntall your updates by some alternative means.
I only plug the internet when I'm FTPing, other than that I keep it unplugged as often as possible. I don't trust $ony, they're sneaky D: They'd figure some way to jb users over eventually, and I'd rather be safe than sorry.
Anyways, I tried turning my ps3 off one time and I came back like 5 mins later to find it still on, but doing some weird stuff, so I unplugged it from the back xD Call me paranoid, but I swear it was like trying to auto-update even though I have that off.