No. All of the "running" QBs in the NFL can also throw the ball pretty damn well. The elite of the elite NFL QBs are still largely drop back passers. Aaron Rodgers is the only tier one NFL QB who can be considered dual threat, but compared to the likes of Cam, Kaep, Wilson, and even Luck he's not that level of runner.
A running QB definitely adds an extra wrinkle, but so does a QB the level of Manning, Brady, and Brees (ugh).