I was trying to figure out how I could receive calls while using a LOD and an external mic (I have a Monster iSoniTalk) with my iPhone4 and I came upon this:
After doing this bit of light reading, I decided to try just connecting the adapter directly to one of my Total BitHead's two output jacks. It works exactly like mnagali says when using a splitter - apparently the BitHeads just use a basic Y adapter internally, so if you feed the output from another source into one side, you'll get it back out on the other. I would assume it's probably the same for any other multi-output headphone amps, except of course for any that might have independent amplifiers.
Audio quality seems unaffected (based on a few cursory tests so far) since, for everything but phone calls, you're still feeding the amp via the LOD. As for calls, phone use is very forgiving, so as long as there're no problems with the mic adapter or the cable going into the amp from there, everything should be fine. I didn't notice any drop in quality, but then again, it's not like there's a lot of nuance in cellular voice quality to lose.
What I DON'T know is if this will have any negative long-term affects on either amplifier (the BitHead versus the iPhone's internal amp.) I would think that, as long as there are headphones connected, this should be perfectly safe since they will present enough of a power drain to keep one amp from overloading the other. Any ideas on that?