Answer: It depends.
Explanation: Among teams with less than 50 QB rushing attempts in a season, QBs averaged considerably more passing attempts and passing yards than teams with more than 100 QB rushing attempts in a season. Non-QB rushing attempts on low-QB-running teams narrowly exceeded those of high-QB-running teams, and experienced a slightly more significant edge in non-QB rushing TDs. In other words, although the disparities were not huge, and there were clearly exceptions, these results generally aligned with popular opinions. But in addition, high-QB-running teams averaged more non-QB rushing yards and more TD passes than low-QB-running teams.
Why This Matters: Conventional wisdom would suggest run-heavy QB teams adversely impact RB and receiver production. But it's more complicated than that, meaning rostering an RB or receiver on a run-heavy QB's team might not be as risky as it first appears.