From his findings, they do not. We should note that this work hasn't been published in a journal and hasn't been subject to peer review, but this side project of Bergquist's seems to show that there's very little connection -- if any -- between film success and Rotten Tomatoes scores. For 2017, which has been a pretty bad year for movies so far, there was no significant correlation between Rotten Tomatoes scores and box office revenue. That measure took into account the 150 movies released this year that grossed more than $1 million.
And while film execs are quick to point the finger at critics, Bergquist found that over time, critic and audience scores on Rotten Tomatoes have started to converge, growing increasingly inline with each other over the past few years. The post goes on to look at how budgets and things like CGI have affected film performance and critics' scores, all of which you can check out here, if you're interested.
Again, this isn't an official study and Bergquist notes that there are complicated factors at play here. But it's probably safe to say that executives should spend less time blaming Rotten Tomatoes and more time making better movies.