I've had 3 pairs of pig/rabbits living together (before I knew any better) and we fed them GP food. They always did well together.
I have a rabbit and 2 guinea pigs now, they live apart, however I do let them play together, and they have done since Rosie rabbit was a baby. She has grown up around them and hates rabbits, but is so gentle and loves being with the GP's and they love her to bits and snuggle with her.
But I wouldn't house them together. Playtime and run time together is fine in my opinion as long as the rabbit is gentle and has always know pigs.
Everyone mentions the damages rabbits can do to pigs, but a lot of people forget how dangerous pigs can be to rabbits. They can be viscious to them, pulling on their ears and tail, and biting ears as well.