No, but if you have a USB mouse and keyboard, you can always try plugging them in to see if it works... But really think of the PS3 web browser as a gift for those times you need to look something up kind of quick and are too lazy to get off the couch and go to the computer, not as something to be used regularly.
Otherwise, plenty of places are trying to offload refurb 80GB consoles that should be capable of installing Linux. You could have one system for Linux and another for gaming.
I realize, late, that the Slim doesn't have an option to install Linux...even though, I quite happy in general. But I found the internet browser really annoying...there's a way to download an different browser?.