Actually the answer is yes and no.
If you are shooting normally with the viewfinder then once you go smaller than f5.6 as teh detected maximum aperture for a lens (or lens+teleconverter combo) then the AF won't engage.
If you are shooting with live-view though the limit shifts to f8; though the live-view AF is a different setup so it might or might not be as reliable/fast.
Note you can "tape the pins" on a teleconverter so that the camera doesn't see it attached; the AF will thus engage, but as mentioned above, its speed and reliability will become less and you'll want good light to work with. The reason partly for the limit is that the mirror assembly sends light up into the viewfinder, but also reflects a portion down into the AF sensors; so the sensors only get a part of the light to work with, not all of it. The live-view though gets all of the light (as there's no need to reflect the light anywhere else) which is why it has a greater range of limits to work with.