Not really. It's only dependent on stock prices inherently reflecting all of the information buyers and sellers have about their expectations, including expected risk and reward. Trying to "time" the market basically means trying to find a signal other buyers and sellers haven't figured out, or at least not enough of them to cause prices to shift accordingly.
Which isn't to say it's impossible. You can be among the first to notice something is awry. It just probably won't be "the P/E is off"; lots of people look at that. It'll be something like in the last housing bubble -- "huh, I noticed housing prices are way out of reach for median income earners, so I looked into loan practices, and apparently risky loans are being repackaged and sold off in a way that masks the risk" and then watching things like loan default rates like a hawk, and then selling as soon as loan defaults started affecting the market.