Is sleep an adverb

No, the Word "sleep" is either a noun or a verb depending upon how it is used in a sentence. For example:

My sleep was interrupted last night by a loud crack of thunder. (noun form)

I'm so tired I will sleep well tonight. (verb form)

The adverb form of "sleep" would be "sleepily". Example: The child sleepily wiped her eyes and yawned loudly.