I think part of what's important in morphing is not only the genetic component, but how you imagine yourself to be as well. If you're injured and you demorph, the injury goes away in part because the injury isn't part of your default self-image. This property of morphing that's separate from mere DNA (which is never really explained in the series, but must exist) is responsible for things like maintaining a haircut, morphing clothing, and other more subtle things. Another that comes to mind is how the Animorphs are able to morph into animals that need to maintain a complex broth of specific bacteria in their guts, such as cows, in order to stay healthy. I presume that since the bacteria are such an integral part of what makes a cow a cow, they are somehow conjured out of Zero Space along with the rest of the cow when morphing.
For a disease like Crohn's where the genetic component isn't enough on its own, I think it would depend at least partially on how you subconsciously imagine yourself to be. If the disease is something you've had since birth, then it's likely to be permanently ingrained into your self-image. Therefore I'd wager that it is not something you could get rid of by morphing.