I always wonder at this point what magic amp is inside a guitar amp which actually is different than all the amps the are made by Crown, Denon, or anyone else to lead to these types of statements. Or what's so different about a late '50s Fender Bassman compared to an amplifier and quality speakers today.
When people listen to a good recording of someone playing the guitar, on their home system, I now wonder why the speakers just don't blow up and sound lousy?
I think the key in all of this is the proper conversion from what's coming out of the guitar to a voltage and range which is in line with the home theater system. If you are overdriving the inputs, it will sound horrendous, and if you don't have a proper guitar preamp (or it sounds like it may actually need to cut gain), then it wouldn't work.
Either way, the OP seems like they may be on quite the budget, and there likely isn't a way to get good sound into a HT system on a budget. You need the equalizers and proper connections to deliver the best sound. The electric guitar side is certainly not my area of expertise, but I'm still at a complete loss as to why distortion from a guitar would damage my HT system if fed at the proper levels when distortion from guitars in basically in every CD I own. It's not distorting the stereo or speakers, they are just playing back what's fed to them, without clipping, but accurately. Shouldn't they?
As for sounding like a guitar through a guitar amp... I really have no idea if that's a good or a bad thing. It may be like saying "nothing sounds like a record playing on a good record player", it's certainly the case, but good or bad is still questionable.

All meant in good nature of course and I'd be more interested in hearing it all both ways and then making more of an informed decision.