Can an ordained person keep a late sleep schedule? If a person has health reasons that make sleeping late (say, 3am-11am) a necessity, can such a person appropriately hold monastic vows in the Geluk tradition of Tibetan Buddhism?  Are there certain sleeping restrictions mentioned in the vows?
Yes, such a person can appropriately hold monastic vows in the Geluk tradition of Tibetan Buddhism. There are sleeping restrictions in the Vinaya, but not regarding the time or length of sleep. Although Vinaya states that sleep is an impediment to the three trainings, in any case over-sleeping (are 8 hours of sleep over-sleeping? this is open to interpretation) would not constitute a downfall since it is not the breaking of a vow.

However, sleeping at such hours and for so long would be seen as inappropriate by many. In addition, a monk could hardly stay in a monastery or in a center (even in the West) with such a schedule, because there are (1) monastery-schedules, and (2) rules that are not Vinaya but institutional. It is not rare to have pujas in the morning, etc. Of course, Western institutions are not as strict as  the Tibetan ones (for Tibetan have to wake up at 5:30 am, and if they do not, they are fined by the disciplinarian) but still.

Most of the western sangha are relatively wealthy elderly women who live in their houses, enjoying various floors, living with their cat, great gardens and the like, on their own, and not all taken that seriously by monks.

I suggest you read Lama Yeshe's Advice for monks and nuns.