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Since the probe's radiation resistance is closely related to in characteristic impedance. And the vary with the same trend when its dimension varying. So the answer is yes.
But can I ask why you are concerned about the probe's radiation resistance. For my experience, that is the value that we usually neglect.
Re: WG/coax transition: probe radiation resistance vs diamet
I agree there's a similarity to the radiation resistance of an antenna. But it's not a common term in
waveguide technique. Actually length and diameter of the probe stud both influences the impedance
matching. You'll also find alternative transition geometries in literature, that are said to be better suited
for high power, e.g. the lower waveguide transition in the below illustration.
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