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

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.