I've had 3 greyhounds & despite them spending most of the time like a living rug its not quite the same without a ninja pointynose (excel at stealthy sneaking up and stealing any food items) round the house.
Some dogs may have come back from a home or been in foster. Mine came straight from the trainers & hadn't had any home experience, if treat it like having a puppy with toilet training, being gradually built up to being left, household noises, stairs, socialisation (other dogs -Many won't have seen anything other than greyhounds, strangers, road noises, children, animals etc). Its easier than having a puppy & adult dogs don't need to toilet as frequently but training the basics are same.
They've raised beds in kennels so sofas are appealing but not all will try to get on & can certainly be trained to stay on their own bed. My boy perked up at the sight of all the sofa's in DFS and was sad we had to walk by to Pets at Home
.
I think a lot depends on the rescue you get your greyhound from as some put a lot more effort into taking the dogs out into more normal environments and assessing behaviour for kids/dogs/cats. Some stay at fairly rural kennels and may not even pass other dog breeds if walked off site.
One thing which I think should be mentioned more to new adopters as would hopefully then avoid any incidents is whats known as sleep startle/aggression. Its where may air snap a warning if woken suddenly (I.e to kennel mate whose probably just trampled over them) & as they often sleep with eyes open that can confuse people, kids especially who are most likely to be leaning in touch during the air snap & contact becomes a bite.
It's easily managed for those dogs and does tend to decrease as they become accustomed to being woken up, but high risk is early in adoption so leave dog be if laying down and always call to wake first. If you need to move dog off sofa or take something off them, use food as a trade.