Hi, we've got three greys and do a lot of voluntary work with them too. Obviously, there is quite a difference between individual dogs but some generalities would be:-
Yes, they are generally very healthy. They are bred to work not to show, so are in pretty good shape. Typical life expectancy will be to mid teens, sometimes even older. Occasionally you will get a grey that may have an old racing injury, but usually the rescue will know about this (often this is why they've stopped racing) and for being a pet, they will be fine.
DON'T expect a lively, bouncy, full on dog who wants to play endlessly with your children, walk for three hours a day or will be bored if not doing a Krypton Factor puzzle twice a day. They are not the brainiest of dogs (being kind here 
), are very gentle, sensitive souls and generally like to spend the day resting peacefully with a couple of shortish or one longer walk each day. They will usually colonise your sofa, bed or other comfy spot (being so bony!) and will lie there, farting contentedly with all four legs in the air. Usually their working life will mean that they are used to being handled, travel well, are good on the lead, and will "learn" housetraining in a weekend.
Depending on if they've spent time in a foster home, they may need to be introduced to things like hoovers, stairs, washing machines and so on. They may need to be taught to "play" having never had that in their racing life. Once they get the hang of it, they become utter love sponges, who are always up for a cuddle and are deeply affectionate, doing a "power lean" when wanting some fuss.
Possible downsides - firstly, they are very addictive. Second, prey drive. Greys are bred and trained to chase small fluffy creatures and don't always distinguish between lures, cats and Yorkshire terriers. Generally a rescue will assess a dog's prey drive and will let you know if the dog is cat safe/small fluffy safe - most can be safe with other dogs and around 20% will be cat safe. You should be aware of this chase instinct though since it is hugely powerful and can over-ride even very careful training. So you should only let them off lead where you are pretty sure you are safe if they suddenly see a paper bag half a mile away and decide to run. And when they run, they are very, very fast indeed.
In winter and in cold, wet weather, they will need to wear a coat, and they will need a proper sighthound collar. They can escape from normal dog collars and they can break their necks if they suddenly decide to accelerate, while wearing a colllar that is too narrow.
I have deliberately overstated the negatives - many families with greys let them off lead quite happily and will have them co-existing with other pets. But I think it is better to be forewarned and also to remember that while many dogs chase cats, for instance, greys are so fast, they can catch them.
Please feel free to ask any more questions- would be happy to talk about them for hours! 