Kaufman will lose pretty easily against a 1800 player with knight odds, me too, of course. Talking about 1800 FIDE, not USCF, which is inflated by 100-120 points, at least.
Speaking as a player who is actually the equivalent of the 1800s in FIDE rating, I could easily see myself gradually making enough mistakes to give my GM opponent a gradually better position, resulting in some sort of position where my opponent may have won a pawn back and created some kind of fortress situation where despite my piece it's so hard to break through without precise play. If I were to predict my result in a piece odds game against GM Kaufman, I would be slightly leaning toward a draw, although a win would be possible; also note, I would even consider losing that game a definite possibility.
Having approximately the same rating as Kaufmann, I can safely declare that winning ONE game out of ten with knight odds against a 2000 FIDE rated player would be a great achievement, actually I would be proud of it.
Kasparov could do much better, of course, but still the odds would be heavily against him. A piece is a piece is a piece, and a 2000 FIDE rated player is not a genuine woodpusher.