This is a real simple question to state. I suspect a precise answer might be difficult to give in the absence of a lot of math, but I’ll try anyway.
Acceleration is indistinguishable from a gravitational field according to General Relativity. Charged particles undergoing acceleration emit electromagnetic radiation. So does a gravitational field also cause a charged particle to radiate?
Do you mean basically does a charged particle, sitting on the surface of the Earth, for example, emit radiation due to the equivalence principle?
The answer can get a bit sticky, depending on how deep you want to go, but an important point to realize that if a charged particle is subject to uniform acceleration then a co-moving (Rindler) observer does not detect any radiation from the particle, even though inertial observers do. Similarly an observer sitting on the surface of the Earth would not expect to detect any radiation from a nearby accelerated particle, though it is possible there may be some very tiny effect due to the fact that an em field is spatially extended.
I assume the answer is that because the gravitational 'acceleration" force is 9m/s^2 and with detectable radiation we’re talking relativistic speeds and acceleration changes… not detectable but theoretically yes.
So then, would a particle radiate as it falls into a black hole? IIRC, yes…