Yes. The desire exists. There's just nothing to back it up
Yes that emphasizes how I do not think this terminology makes sense. If you want to say that the type of desire cannot be definition be filled for some reason, then that's one thing, but the word "empty" seems to me to have nothing to do with the discussion.
If we feel the desire, it exists. Maybe the issue is in the definition of desire. I consider a desire to be a feeling, not concept. I "feel a desire" - I don't "feel a concept."
If I can feel something, then it exists, and the word "empty" comes dangerously close to asserting that the feeling does not exist, which would almost certainly be inconsistent with the rest of Epicurean philosophy.