If you are really strapped, it would work provided you take your signal outta a headphone or line out. It'll sound like crap, but there'll be a signal. HOWEVER, DO NOT PLUG THE SPEAKER OUT OF YOUR AMP INTO ANY LINE LEVEL INPUT!!!
EDIT: This will only work with dynamic mics BTW, condensors need phantom power.
A lot of things are possible... doesn't mean you should do them...
And I've never seen a 10 watt practice amp with a line out... but then again there's a lot of things I've never seen...
It Worked.My amp has a pretty good eq built into it.I took the headphone line out and ran it into my mixer.It seemed to work pretty good.I used two microphones to mic my amp then ran each into to my guitar amplifiers.Then out of the headphones output into the mixer then into my multi track.
We used to record our band practices in much the same way you described. Believe me when I say you can do better....a lot better. Depending on what you are expecting to get out of your recordings, I would recommend getting a cheap mixer like the Yamaha MG at the very least for you preamping needs.