It depends on the situation. You can't just say, "you're out if you miss the playoffs". What if they go 10-6 and find a long-term QB (either Mitch or whoever they sign) but Khalil Mack and Akiem Hicks go on IR in September? They could win the division again, make the playoffs, and then get blown out in the playoffs and everyone's fired. If the season is a disaster and they end up 6-10, no QB steps up and the lockerroom is a mess, then sure.
But I honestly think that ownership is all in on Pace/Nagy. I don't think Pace will get another HC hire, but it shouldn't be a surprise if they got another chance to pick a QB in 2021. Plus drafting a QB in the mid-rounds this year that shows promise could buy them time. There's way to many factors than just making the playoffs or bust.