Try it out, does your tv have an analog RCA audio output?
it would say audio out ...
If it does have the output, I would hook it up with an rca splitter on one of the sides, then run a pair of 100hz high pass FMods on your monitors and plug your subwoofer into the splitter before the fmods....
Amazon.com : Mediabridge CYA-1M2F-P Ultra Series - RCA Y Adapter - 1-Male to 2-Female for Digital Audio or Subwoofer : Subwoofer Cables : Electronics
Amazon.com: FMOD Crossover Pair 100 Hz High Pass: Car Electronics
that will make sure your monitors don't get any of the bass your sub is reproducing, so no noisy muddy lows, and it will free up all that power from your monitors to the mid and top end... Then you can just dial in your subs built in cross over to how you think it sounds best.. Most likely around 100...
then use your volume controls to balance everything out.. I think it would be fine, and anything is better than tv speakers..
PS I would buy 2 of them splitters and run stereo to your subwoofer they seem to sound better that way, or split again at the sub...
So its easy enough, you would plug the fmods directly into your monitors, then the splitters into the female side of the fmods, then an rca cable set to your tv and another set to your subwoofer, both of which plug into each side of each splitter...