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.