There is a custom on Rosh Hashanah to avoid taking a nap or sleeping during the day. This does not mean that a person has to wake up at the crack of dawn. It means that once a person is up, functioning, praying, and doing what they need to do on Rosh Hashanah, they should try to avoid sleeping during the middle of the day. The Yerushalmi says that someone who sleeps on Rosh Hashanah will have his mazal (fortune) sleep during the year.
That being said, it is not so much about the segula (auspicious practice) as it is about a person who knows he is being judged in the shamayim (heavens) and that there is a court case against him, but does not feel the gravity of that and wants to do whatever he can to study Torah, do mitzvot (commandments), and do Zechuyot (merits) on the day of Rosh Hashanah to hopefully tip his judgment in favor of the positive. That shows that the person does not understand the gravity of the Yom HaDin (Day of Judgment) that is coming up. Therefore, a person should try to avoid sleeping during the day.
However, if a person is going to just sit around idly and do nothing, then yoshev batel, ke'ilu yashen dami, someone who just sits around and does nothing; it's like he's sleeping anyway. And if a person is doing bad things, like speaking Lashon Hara (evil speech) and doing negative things, then he may as well go to sleep and fortify himself and strengthen himself.
Of course, if a person is feeling very tired and wants to go to sleep so that they can wake up from Mincha and come to the class with enough strength to do the other mitzvot, which they won't be able to do, then common sense dictates that they would be able to go ahead and take a nap. So one has to understand the perspective and know how to conduct oneself with the gravity of the Yom HaDin upon one's head on Rosh Hashanah.