I also like to say that particles don't really exist in any sense one would associate to the word. And to be pedantic, we can't even say that particles are peaks in a field because that is merely how we model it, and that model is incomplete.
Since we don't know what gravity is or does, nor what (or if) a field is or what particles are, it's hard to answer a question like whether a particular field is affected by gravity other than in terms of a specific model and hope that corresponds to real observations.
In this case, our best bet is to reason in terms of known properties of what we think of as particles mediating the field in question. Photons are subject to gravitational influence, and so we expect EM fields to be as well.