The subject of intentional breeding or meat rabbits is prohibited. The answers provided on this board are for general guideline purposes only. The information is not intended to diagnose or treat your pet. It is your responsibility to assess the information being given and seek professional advice/second opinion from your veterinarian and/or qualified behaviorist.
LEADERS: Beka27 BinkyBunny Elrohwen KokaneeandKahlua LittlePuffyTail MoveDiagonally RabbitPam Sarita
A lot of this depends on the level of care provided by the vets at the shelter. In my experience, most bunnies coming out of shelters have coccidia, which is simple to treat, but is very contagious. Many have external parasites too, like fleas or mites. Do the buns receive good vet care at the shelter? Would they pay for you taking a bun to your personal vet for a check up?
I don't really know about the cats, but I would assume that other than fleas, there are no problems that I know of that are transmitted between rabbits and cats. Maybe you could consult with your vet first.