Bots will put something in the field but humans should never see it, so if the server sees anything in there it can safely toss the whole thing.
But other than that, I agree that this is extremely effective against the common sort of drive-by spam bot. (And, obviously, completely useless against any sort of advanced or targeted attack.)
Bots will either hit both or neither and get rejected. Screen readers/toolbars may be an issue, though the names would be hard to think what to autofill with. It has never come up in practice -- the reject message tells people to email us directly
If you have javascript turned off, you'll need to email directly too -- and the site won't work so there probably isn't much lost!