I wouldn't think it would be *that* bad, but I suppose it's possible.
If you use CAT-5 or better, I'd certainly think so.
I really do think you should do the "take the DSL modem out to the demarc and test with a short, good cable" test, even if this means that you have to temporarily move your computer. That's the best way to eliminate the whole house-wiring issue completely.