Would it harm my eyes to go without using them for several hours a day?

You mean sleeping?: Sleep is an important restorative function for humans. Resting your eyes daily (a quick nap) is ok as long as it doesn't interfere with your normal routine bedtime sleep duration.

Ocular rest: No but if you feel your eyes closing during the day inspite of adequate sleep, it could be sign of uncorrected nedd for glasses. See ophthalmologist if this is a recurring problem.