Well - it depends what you mean by "diffraction".
Any point along a wave front will act as a point source of wavefronts travelling radially outwards - so while a plane wave will be arriving at the aperture, the waves that come out from the other side will almost look circular.
To me, that's diffraction. Although there will be no regions where extinction occurs in the way that this would happen for wider apertures.
Here is a picture that describes what I'm talking about:
See also this gif for an animated version
