There were some notable QB to RB conversions in the NFL in the past. Denver's RB Bob Anderson was a college QB, although he actually switched positions during his senior year in college. He was a first round draft pick. As Jaxvid noted, Paul Hornung was a Heisman Trophy winning QB, and Lombardi later switched him to RB.
Ed Podolak's college career and NFL position change mirrored Anderson's- he played QB at Iowa until converting in his senior year and then becoming a full time RB with the Chiefs in the NFL. I'm sure there were other examples I can't recall at the moment.
In this day and age, the reality is that no white running QB is going to be converted to RB. The Caste System is pulling out all the stops to prevent white players from carrying that ball. They will not permit another Peyton Hillis situation to occur. The forbidden dynamic is that of white players running the ball, whether they are conventional halfbacks or read option running QBs.
With so many running QBs in college, it is going to be difficult for tptb to continuously smear every white who excels at the position, in order to keep them from doing it at the NFL level. Maybe even the DWFs will reach a tipping point, and finally, at long last, begin to think and reason.