short answer to your question:
yes it can be used to surf the net.

long answer:
much like the nintendo DS,it(the psp) can surf the net,but it isnt the best device to use for surfing.
it is slow,hardly has memory(you'll be cursing when you reach a picture based site),the in built keyboard is a pain to type fast,etc.

it is best use as a last resort.

comparing my pda with the psp,the pda blows the psp away in terms of surfing speed.

gaming is a whole other matter,though..PDAs just cant compare to a PSP