It doesn't have to be a 4 channel amplifier. But if you run 4 co-axials from a 2-channel amplifier, you will lose your ability to fade front to rear.
What you would definitely want to do was to be sure you wired the left side speakers to one channel and the right side speakers to the 2nd channel. This way you will retain stereo sound. Some people wire both front speakers to one channel and both rear speakers to the 2nd channel....this is a big no-no.
Also be sure that amplifier can handle running 2ohms per channel.
Lastly, are you still using this amplifier for the subs? Because if so you could not use it to power your speakers aswell (well, technically there is a way....but with as cheap as amplifiers are these days you would be better off going with a different amplifier or using the headunit's internal amp).
And no, you would not need a new headunit. If you planned on running two amplifiers from the one RCA output, you would simply need a y-splitter.
