I don't know if that info will be available for a rescue. If the dog is papered you could probably look up the parents and find out if there were cleared but if not it would be hard to tell. I wouldn't really worry about it personally but if it makes you feel better it can't hurt to ask if they know.
One thing you could do is check with reputable breeders to see if they have any older or adult dogs available. I know when I was looking, a lot of them did (either they took a dog back, or they kept one hoping it would turn out to be a show). If you get one from there, they would most likely have the parents records on the OFA and CERF for the parents. We considered getting a dog a year or two old this way, but decided to go with a puppy this time around. Our next dog will most likely be one like that (older pup or young adult).
Buffys mom - thanks for asking. It does get easier with time and I think Mira is enjoying being the center of attention. She is older and sleeps alot so I don't think she is wanting a very active playmate so that is why I am looking at an older, calmer dog to join our household. I think she is pretty, too and very loving.
Agree with CYNLABS. I am also probably going against the grain here, but clearances these days are the least of my concerns. So many other things are happening with dogs these days (especially cancer) that I'd be more concerned with those type things.
Of course, this coming from someone who has all rescues and probably always will!
Good luck on your adoption! I would go with one older than 2 if you want one that is not active, though. 4 seems to be the magic age for becoming a bit calmer.
I also suggest checking with your local reputable breeders. Contact your local labrador club and let them know your interested in adopting an adult dog. If they don't know anyone off the top of their head looking to place an adult, they can usually find out pretty quickly and get back to you. I placed an almost two year old who had her hips/elbows prelimed and eyes checked. Many breeders place older puppies who just didn't turn out the way they were hoping or retire their older girls. Good luck in your search