As the 'E' in P/E stands for 'Earnings,' no. P/E is a metric typically used to measure the valuation of businesses, primarily for pricing equity securities.
There are a variety of other metrics used to look at Bitcoin fundamentals, though at the end of the day a lot of the fundamental analysis of Bitcoin ends up being indirect, looking instead at fiat liquidity factors, and overall risk appetite given performance expectations of other sectors based on their overall backdrop. With bitcoin specific metrics people look at things like how much of the total supply has moved or hasn't moved recently, and of course, where we're at in the halving sequence when it comes to mining. Overall energy supply could play a factor as well, though to the best of my knowledge this is a smallerpart of things aside from massive events such as when China banned mining.
This is all more complicated than what a simple P/E is though. I like to often look at it in terms of fiat cost of bitcoin * 21 M/global population to give myself some perspective.
Right now, that's 21,000,000/8,200,000,000*$89,169.00, for a total of $228.36 for each person's equal share of the hardest money on the planet. Draw your own conclusions with that sort of data...