Hi Russ
SOME 1.4x TC's will fit, you need to be looking at the ones that do not have an element that protrudes into the lens. This rules out the Canon ones, I think you will be OK with the Kenko ones (Not the pro range).
Results - I don't know.
But I don't think it is a decent combination - you will loose AF unless the convertor is one that does not report it's presence to the camera. Even then you are asking your camera autofocus to work outside it's normal operating parameter - will be fine at F4 (70mm ish) but get to 300mm AF will be terrible.