Answering fan questions on the official PlayStation blog, Polyphony's Chris Hinojosa Miranda and Taku Imasaki have said in response to a fan asking whether car damage would be included in the PSP game:
Damage? No. 800+ cars, 35 tracks, on-the-go awesomeness, and a lifetime's worth of racing, yes.
Shame, but there you have it. Those waiting for a touch more realism from their racing will have to wait for the next PS3 game.
UPDATE - On the subject, there'll be no damage introduced into GT5 Prologue, either. You'll have to wait for the final game for that.
Gran Turismo PSP - Your Questions Answered [PlayStation]