Scientifically: There are people from disparate countries who believe that they suffer from a condition called `EM hypersensitivity`, and are convinced they must live in remote areas away from radios to avoid sickness or headaches. In the handful of published studies that exist, evidence points to an inability of these people to distinguish between exposure and non-exposure in a laboratory setting.

Anecdotally: I can definitely "feel" large AC transmission lines. They do have an audible buzz, however the "feeling" sensation seems distinct to me. My experience is from hiking the Appalachian Trail, which spends days outside of cell phone range, and then crosses regional transmission lines periodically.

So if that observation is not pure illusion or auditory synesthesia (perhaps a fully deaf person can assist here?), it would seem to follow that there is a mechanism to sense EM radiation, and it is simply a matter of whether the perceptive threshold has been met, which would obviously vary from person to person and even from instant to instant.