How much can low-fi subwoofer bring down a system?

If you add muddy water to Evian, it might not look as clear or taste as good.

For a more precise answer, it would be helpful to know more about your speakers and the rest of the components in question, as well as your listening preferences.

I agree more details would be useful, but my guess would be that you would have wonderful clear sound coming from your decent componants and a strange thumping, thudding noise coming from the sub (which may be OK if you use this for just HT). It would probably ruin a good thing.
I tried integrating various under $500 subs and never found one that integrated in any acceptable way with the Linn Tukans I had (activ with LK85 amps). It took me a year to find that Rel subs are a relatively affordable way to get a sub that sounds musical.
Dont waste your time, spend around a grand on Agon and get a used Rel Strata.
Just an opinion.

I use a phase tech power 10 100 watt sub to help out my dynaudio 1.8's when watching movies only. The 1.8's actually go lower but i use the sub to add a bit of oomph in the 35-55 area. I have the hi frequency crossover set to 65 and the gain turned down pretty low so it only turns on when there is an explosion or something. I owned the sub before I got my 1.8's, and found that it's just not fast or accurate enough to keep up the contours. The power 10 is a great budget sub, but I just wouldn't recommend it for a hi end system, believe me you'll notice. IMHO subs should only be used for home theater or in sub/sat combos, otherwise you are better off with a good amp and full range speakers.

I have actually tried what you are proposing on a past system; using a $450 Boston Acoustics sub to complement a pair of Von Schweikert monitors. As Peteinvicta1 predicted, I ended up with superb imaging, transparent highs and well resolving mids, with a nebulous thumping in the lower octaves. Rhythmically confused, intonation challenged, like having a pulsating Nissan out on the curb playing the same track. Completely unsatisfactory.

Don't even think about it. You should be spending at least as much on the sub as you would for one speaker, maybe even as much on sub(s) as you spend on both speakers. Otherwise it just won't match, and in fact, will be a lot worse than no sub at all. If you aren't prepared for this kind of investment, don't get anything at all. Take the recommendation to buy REL, and the bigger the better.