I've actually researched this option. Using compressed air as a structural component is a valid construction technique and could be applied to
hang gliders.
It won't work on paragliders because as ram-air wings, they need to collapse when they get unloaded. Otherwise once unloaded the wing will fall over in front of the pilot and probably get entangled with the pilot.
The only heavier-than-air inflatable aircraft currently in production is the Woopy – http://fly.woopyjump.com/ – its design is very unconventional, with continuously running pumps and some weird flight control mechanism. It never passed certification because it's probably not as strong as other hang gliders.
Some potential problems of inflatable hang gliders:
* Ambient air pressure differences at varying altitudes, temperatures, etc.
* Bird attack – sometimes eagles and other birds can get aggressive and try to claw a hang glider. What is a minor annoyance now could be a dangerous flaw if your glider is inflatable.
* A failed inflatable wing can potentially gift-wrap around the pilot preventing them from throwing the reserve parachute in time.
* Less rigidity than metal tubes – danger of buckling at higher speeds / wing-loading.
* There's a certain stigma among HG pilots regarding the concept of inflatable aircraft due to controversy around Woopy and the general idea of riskiness.
However, inflatable aircraft IS a practical strategy. The shortcomings listed above can be overcome given enough effort.
For example, see http://www.prospective-concepts.ch/html/site_en.htm – click on Projects / Air / Pneuwing (and other projects).
Also, http://en.wikipedia.org/wiki/Goodyear_Inflatoplane
Lastly, in all likeliness the only advantage of an inflatable hang glider would be portability. I don't think it will end up lighter than a tube+fabric construction. The guys from Prospective Concepts seem to believe that they will achieve better glide performance with an inflatable design, but to be honest I doubt that. But then again, they know much more about their technology than I do.