LECA* (Lightweight Expanded Clay Aggregate) is starting to gain a following in semi-hydroponics as well as hydroponics. I'd be willing to bet money that Griznatch's wife is growing orchids semi-hydroponically, which involves putting the orchids in a container filled with leca balls and adding RODI/distilled water and some nutrients into it (typically the hydroponic kind). I'm currently doing some web searches on whether or not if it's useful to use in larger plants such as gingers, birds of paradise, and lobster claws. Perlite is a known substitute for LECA, although LECA tends to have better aeration.
IF the ecocomplete doesn't compact, then it could function as a LECA substitute. However, the way I've learned to use LECA was with a dual pot system: a net pot to hold the LECA (or LECA substitute) + the plant, and a cache pot to hold the nutrient water reservoir. If the ecocomplete is too fine, then it might just...leak into the water which is counteintuitive to planting a plant.
What're your thoughts on using it to start seeds? I've never used ecocomplete before, but I've thought about using it from time to time. If it's easily fluffable, then it could be a good seed starter.
As for carbon: it depends. Are you using it just to adsorb random chemicals in the water? Or for the express purpose of adsorbing a certain medication? If the latter, I'd probably bleach it, and toss it in the trash. If the former, I'd consider the following:
using it in fire (? needs more looking into, but once dry may be an adequate fire starter)
experiment with fluidized bed filtration
As for tossing it in the garden: There is absolutely nothing wrong with "tossing" it as long as you haven't medicated it. It's better than in the trash where it goes into the dump and just lies there for forever waiting to be broken down. Plants can utilize it eventually.