Due to Einstein's equivalence principle, I think this is not the case. In the Liénard–Wiechert potential (which describes the em radiation of accelerated charge) I do not see the source for the acceleration - but it has to be there since otherwise, it would be independent of the source (gravitational source or electric/magnetic field).
So, my question is - where in the Liénard–Wiechert potential is the source for the acceleration, and would another source (gravitation) cause the same effect?