RMS is what you need to worry about. Your subwoofer can take 400 watts RMS @ 4 ohms. Your amplifier supplies 200 watts @ 4 ohms. Ya, it'll work but your only giving your subwoofer half the power it can take. Seeing that you don't know that much about sound audio and such (no offense, not trying to be an ass at all). I'd have to suggest that you stay with that system. My reason is because since your only putting half the power into the subwoofer as it can take, it will last alot longer, which means you won't have to replace it sooner, so you won't have to deal with it.

Course you could just give it 400 watts RMS @ 4 ohms with no problems, but in your case I think having a subwoofer to start with will be a big jump.

how much you paying anyway?