Can there be a mental disorder where the afflicted believes they're younger than they actually are?

Maybe. People with multiple personality disorder (mpd) have distinct personalities that "take over, " depending on the situation they are facing. Some of those personalities can be quite young, and the person when in that state certainly will act young and may believe her or she is whatever age that personality is.
Not specifically. There are situations where people act much younger than their age, most often related to developmental disorders or significantly reduced intellectual capacity. Dissociative disorders on occasion regress into childlike behavior and speech. None of the above involve the individual actually believing they are younger than they are. Others may simply pretend they are younger and know it's not so.