Though in classical field theory photons are not emitted or absorbed instantaneously, the energy dispersion (Poynting vector) of the antenna near-field travels slower than the ultimate speed limit.

I have no idea how it translates to photons of the quantum electrodynamic field, but it would be odd if there isn’t a close map to the near-field effects. (While I would guess that either the photons appears massive there, or — less likely — doesn’t appear until at some less well defined border to the far-field.)