Picture yourself floating in deep space. Suppose you observe a charged particle with non-negligible mass accelerating. I wonder if there is a sure-fire way to tell if the charge is accelerating due to gravity or some electric field.
I think it is sufficient to check if the charge is radiating or not. If it is not radiating, then it is accelerating due to gravity. If it is radiating, then it is accelerating due to electric field.
If it is accelerating because of an electric field, a nearby test charge with the opposite charge will accelerate the other way. If gravity, the same way.
The core concept to answer this question is that, whether we are speaking about charged particles or any other mechanical system, there is no way to tell the origin (interaction) of a given accelerated motion without additional information. Simply observing an acceleration without the possibility of performing experiments on the accelerating body and the environment is not enough to establish the origin of acceleration.
From a more formal perspective, the previous statements are justified by the difference between knowledge of acceleration as a function of time or of all the parameters the interaction depends on. Notice that such a difference is theory-independent. It remains the same in Classical Mechanics, Special and General Relativity.
From the GR point of view, one could think of using the presence of a radiation field as environment to exclude or not a free-fall motion. Unfortunately, this is not the case. As it has been explained in this answer by A.V.S., a free-falling charge will radiate in any case, because cannot move along a geodesic, due to the presence of the electromagnetic field.
If you are floating in deep space you cannot see a nearby particle accelerating due to gravity, because gravity will accelerate you as well. So if you see a particle accelerating relative to you, it must be due to an interaction that you don't participate in. That it, electromagnetic.
