Could it hurt my grad school application if I state a secondary research interest in which I have little experience?
I seriously doubt it will make much difference. You say you primarily want to work on Y, and your research experience is in Y, so you'll be judged as &quot;a prospective Y student.&quot; If applying X to Y is a reasonable thing to do, then saying you're interested in X shouldn't hurt you at all. But without any real background in X, it also probably won't help you much.