Hybrids are more likely to be healthier than their parent species as long as the parent species are closely related. As is the case with eclectus, since they are considered separate subspecies rather than separate species, hybrids within them should be just as healthy, if not healthier (genetically speaking) than their parent species.
Honestly, the only health problems that I have heard about are from hybrids between large conures and Pyrrhura conures and some multigeneration/multispecies macaw hybrids. I have yet to hear of health problems in lorikeets, conures of the same genera, poicephalus, pionus, ringnecks/psittacula, rosellas, barnardius, grass parakeets/neophema, polytelini tribe, cockatoos, amazons, large conure/macaw hybrids and large conure/amazon hybrids... although the last one is one of the lesser known hybrids to occur so not as much is known about them.
I suspect we still have a lot to learn about hybrids and species!