No, it is not.

I may be wrong, but I have never seen any provider-locked phone in the whole country (Italy, I mean), and they may very well be illegal.

All that phone companies do, sometimes, is to put their logo on mobile phones. But you can still use them with other providers. There's actually a different market for "branded" mobile phones, which people buy because they're less expensive (nobody likes the brand on them) and use with their provider, whatever it is.

Edit:
This P800 is not branded by any phone company. It only hs the SOny-Ericcson logo/brand on it.