no, it won't a PSP doesn't have enough RAM or
Wait...Dude, you don't have a sister...(Sorry, I had to) If you have wifi and connected to the internet, shouldn't you be able to just go to the website, sign in, and play?
I would suspect not since it's an online game and really should show on a bigger screen. But if you google "club penguin psp" you will find several links to downloading a version that is supposed to play on psp. Good luck.