There aren't "many" psittacula hybrids, so I honestly can't say... there are hundreds, if not thousands of indian ringneck x alexandrine hybrids... which I've never heard of any health issues in. Breeders in Australia used that hybrid mix to cross mutate mutations from IRN's to alexandrines. There's also ARN x IRN - but they're considered the same species, separate subspecies.
The following page lists some Psittacula hybrids, including the derbyan x moustache hybrid... which it appears that the hybrid leans towards a derbyan but with a lovely plum colored chest.
The Pyrrhura x large conure hybrids (so far, all Aratinga to my knowledge) are a bit of a "rarity", in that most hybrids are born healthy, and worse case, are born with infertility. The Pyrrhura x large conure hybrids are often (but not always) born with birth defects and who knows what else. Some have lived for at least 5-7 years, one if he's[?] still alive would be 13 now? (green cheek x nanday - to my knowledge is still around but that could have changed). There could be some (sun x green cheeks) older than that one.
There's also been birth defects seen in nanday x hahns, potentially in sun x hahns (multi-gen hybrids - might include jendays - hard to say how much is from hybridization, how much potentially from inbreeding), and some hybrid macaws, too.
Beyond that, you really don't see health issues/birth defects in hybrids....
Although I do wonder about King Parrot x Rainbow Lorikeet.... that is an odd mix! Or perhaps the Jardines x Timneh... or Conure x Amazon hybrids... or Caique x Conures...
I'm beyond excited!! I actually put 2 videos of him that the breeder sent to me onto my youtube @TropiKate 
