
So long as you can stay aware that they are generally (although not always) TOTALLY unsocialised and quite 'backwards' in their education regarding ANYTHING other than running really fast, being kennelled and travelling in a van or car, you should do ok.
Life as a racing dog is REALLY insular, so dont be at all surprised if your dog doesnt recognise 'non pointy' dogs as being dogs (an beware the very small fluffy jobs!!!), stairs, as mentioned might be an issue, as well as every day household sights and sounds.
Just take it as it comes, start from scratch as if you had an 8 week old puppy wrt housetraining and socialising.
A basket muzzle is a must, but DONT get into the mindset of thinking your dog is inherently a killer -- he is not, any more so than any other undersocialised dog, the only difference is, HE can catch things he chases!
Likewise, dont think you cant train a greyhound, you can (althuogh i wouldnt be expecting top class competition obedience), including a recall, IF you put the work in (and i say this as many people just go 'oh he is a greyhound, he cant do recall). and bear in mind that whilst wearing a muzzle is a sensible precaution to take, it cannot prevent him chasing/scaring and headbashing his 'quarry' should he choose to do so!
All the ex racersi have met have been lovely laid back dogs in theend, although some take more work than others.
My own dog had a similar background, but as a working lurcher -- undersocialised, kept in a shed, didnt understand how to be a dog. Fortunately she ahs (for a saluki) a good recall and ive learned to read her body language damn well -- she can be around my cat but i still have to tell her to leave him if she gets too keen. Other cats, no way!
Good luck
Em