It is physically possible. Home theaters are intended to optimize a recording upon playback, and to emphasize low end effects. It would be a terrible medium for mixing, and extremely difficult to get mixes that translate well to other systems.
Unless you have a very neutral sounding system (unlikely) you may even be better off with a combination of headphones [spits] and computer speakers [spits again].
Back in the day...I did my mixing through an AIWA stereo system. It is less than professional, without a doubt, but it worked for what I was doing. If you're wanting something just for listening it'll be ok. If you are trying to get something ready to sell, it'll suck.
