Sleep deprivation is not as dangerous as dying from an acute condition. If you're in the hospital for one night, you're being treated by doctors who want to make sure you're not going to die for the night. If you get admitted for a longer period, it's a different environment altogether. At least this has been my experience.

You get used to the beeping after one night anyway. If not, you can ask the nurse for earplugs or even sleeping pills (although sleeping pills are harder to get).