No, don't ever, ever eat a town-rat pigeon! However, the wood pigeon, fed on food not Mcdonalds litter etc, is indeed a mighty tasty thing!
I have discovered a couple of these are LIVING IN MY LOFT and I'm not happy about it. There's a hole which I can't get to in the wood around the gutters, so I fear that any eviction attempts won't work unless I can find a friendly person with a very tall ladder!
I haven't quite got the guts to trap or otherwise kill them though. Hypocritical, i know, seeing as I've enjoyed eating many of their relatives!