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

All things being equal, how much can a low-fi, circuit-city, subwoofer bring down a system with fairly decent components? Will a more high subwoofer make THAT much of a difference?
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.
Besides the REL, if you want a sub that uses a high pass crossver (so that your speakers and amp don't handle bass below, for example, 85 hz) consider a Velodyne servo sub like the FSX 12 which can be had used for around $600.

When I compared subs, some less expensive models (including Velodynes) weren't bad, but to me they still muddied the sound somewhat.
It will make your system sound bad. Timwat's delightful description is right on the money. I tried a high quality $1100 home theater sub with my $9K audio physic speakers and the result was terrible. They were completely out of sync speedwise. The sub did sound good on my television with some $500 midfi speakers. They had drastically different voicings - one made for muddy boom, the other made for knife edge definition.

Later I aquired a rel storm I and found that to be light years ahead. I have since upgraded to some full range avalons, so I don't use the sub very often anymore. Sometimes it's nice for blues music.

If I wanted to go cheap, I would consider:
- an older rel,
- velodynes and vandersteens
- Some of the much older smaller subs such as Prosound or spendor.
- The smaller HSU that stereophile/TAS raves about ($500 new)
- DIY sub from madisound or adire audio.

Note that older subs may need woofer surround repair.
You might want to check out the ACI Titan sub.
I too am thinking of getting a subwoofer to augment my main speakers and the concensus seemed to be either a REL or an ACI sub. RELs may be auditioned at a local hiend store while the ACI is factory direct but they do have a 30 day in-home trial period. I've heard lots of good things about both subs but if i had to decide i'd probably roll with the ACIs because of their cost(~$1200) and also because i'll be helping an American company.