I'm in no way an expert on this. But i'll tell you from personal experience what has happened to me.
I had originally hooked up my subwoofer to my 6 channel amp running 4 internal speakers off of it too.
It fried two JL subwoofers.
The first time one of the voicecoils fried and broke off. The second time it just stopped working.
So I got a new alpine 500watt amp for the sub, and it's been perfect since.
I guess the moral of the story is that it does matter, and you can't just hook it up to anything