What a great question. It is similar to asking, “Can someone who has never seen before imagine what it is like to be able to see?” It is a difficult thing to answer because our brains evolved to keep up alive, which is rooted in our senses. We never had any reason to develop the faculty of imagining a new sense.
We dream within our senses, so to speak. We “see” and “hear” things in our dreams. But that doesn’t mean that we have a “new sense.” Even when we imagine we are playing a musical instrument, PET scans of the brain show that the same planning centers in the brain light up as if we are actually playing it. When we imagine seeing something, we are using many of the same parts of the brain as when we actually see it. So it isn’t so much of a new sense as it is simply an annotated version of the senses that we already have.
Therefore, so far as I can conjecture, imaging a sense requires the blueprint for that sense to already be there. The closest I have heard of someone imaging a sense that is beyond what we can perceive is what some people experience in altered states of consciousness or after suffering damage to the brain. For example, in synesthesia, people report tasting colors or seeing sounds. Yet, this isn’t so much imagining a new sense either as much as it is just altering the ones we already have. Some people report feeling a sense of oneness with the universe while on psychedelics or while meditating, however, this is more of a diminishing of the sense of self than it is perceiving an entirely new sense.
Try another experiment; just imagine that you have the ability to perceive the radio waves from all the radio towers in your area going through your body. Just try to imagine what that would be like to be able to perceive it. BUT, you are not allowed to substitute any of your other senses; it must be a new sense. Chances are, you cannot do it without it being similar to another sense. Maybe you imagined “hearing” all the music and voices of those radio stations going through the air. Or maybe you “felt” a tingle in your body as the waves coursed through it. Nonetheless, you were simply using existing senses to perceive something that you don’t ordinarily perceive. It was not a new sense.
I would say that anything that the brain imagines, it must have a current blueprint for it. Anything new that is experienced, the brain will interpret it through the lens that it has.