Every car audio headunit I've worked with supports 4 and 8ohm with no problem. Very few work at 2ohm safely and won't put out enough power for a sub, most modern units being around 15w RMS.
The issue still stands with the factory amp: It is not a traditional amp, more of a processor. The factory amp is the fade, balance, volume, and EQ of the factory unit. It has a simple left and right input and uses feedback from the factory radio to work. If it would produce any results, I couldn't begin to guess what it may be. I didn't check the voltage level of the inputs when I did my replacement, and a headunit may overpower it quickly.
I haven't messed with it, but some people have had luck with small aftermarket amps and Line Out Converters (LOC) from the rear channels. You may have some luck searching the Electrical subforum.
For reference: The factory system is actually 8 channel output. Fronts, dash tweeters, rears, sub (DVC).