Is "best" an adverb?

Best in your example is simply an adjective filling the role of the subject predicative. It describes the position of the speakers (‘in the best possible state’) if they are undisturbed.

I think this is a highly colloquial phrase which defies typical grammatical standards. Best is an adjective, and better is usually an adverb. To express the above sentiment with grammatical precision, one would have to say, "We are better if left alone." I think analyzing colloquialisms can be intriguing, but rarely results in an especially clear understanding of the underlying structural principles of the sentence or phrase.