With physical handicaps, yes, I believe that the morpher would gain whatever disorder it was. Blindness, cystic fibrosis, they would get, because that's part of the body they'd morphed.
Mental handicaps would probably be a bit different, though. Keep in mind that, during a morph, the morpher's mind is connected to the morphed body via z-space, which is how they can fit human intelligence into the brain of an ant. So mental disorders probably wouldn't carry over, because the morpher's mind stays intact and connected to the morphed brain at a distance. I'm not an expert, but doesn't cerebral palsy affect the nervous system? If it is a mental condition, then it shouldn't affect the morpher. If I'm wrong, though, and it's muscular, then I think it would.
Hmm. If my theory is right, morphing could be used to test disorders that are of unknown mental/physical origin. Like people suffering from chronic pain or something.