hey mate how's it going? No... don't go doing that - bad idea. I have no idea about what power output your amplifier/speakers/sub has so i can't comment on whether it would be a POWER overload, but your average speakers operate very differently to a subwoofer. A subwoofer is designed to reproduce low frequencies (usually around the 20Hz to 100Hz) which is your "sub-bass". Your speakers on the other hand are designed to produce higher frequencies stretching up into the thousands (for example from i dunno, as low as 65Hz up to 20,000Hz).
If you had them both hooked up to to the same channels, you would have a problem depending on how your amp filters were set. If you had it say set as a low pass filter at 100Hz (will produce all frequencies below 100Hz but nothing above it) then your sub would be fine, but your speakers would be being made to produce frequencies too low that they weren't supposed to be and you will most likely damage them (not to mention a crap sound because you wouldn't hear anything above 100Hz so you'd pretty much have no music). If you had say the high pass filter set to 100Hz (produces all frequencies above 100Hz and cancels out the rest) then you'd end up making your subwoofer attempt to produce frequencies that range in the thousands, perhaps up to say 20,000Hz (which is certainly not healthy for a subwoofer and once again, will sound crap and almost certainly cause damage).
For what you want to do you'd want either a single 4 channel amplifier or add on a monoblock (1 channel amp that's pretty much designed for subs) and run the sub independently off that (if you chose a 4 channel you could have 2 channels for a pair of speakers and bridge the other 2 for a subwoofer). I don't know about your setup, but you'll find that your best to be amplifying front speakers (preferably splits) first (if you have any) rather than rear speakers as rear should only be providing some sound "fill" rather than being right in your face and most of your music should be coming from "up-front". So if you really don't want to buy any more equipment but want that sub i suggest you change your rear speakers back to running off the headunit and THEN bridge your sub off the 2 channel amp (making sure to set the low pass filter etc). Anyways, hope this has helped, cheers, Bryce.