The period over which tidal locking would occur is highly sensitive to the distance between the bodies, and varies by the distance to the power of 6. It is less dependent on the mass of the primary. The relationship ( assuming all else is equal) is T = a^6/M^2
So, if we take a very luminous red dwarf like Lacaille 8760 with a mass of 0.6 that of the Sun, and a Earth equivalent position in the habitable zone of 0.268AU, you get a time period for tidal locking of roughly 1/1000 of the the time it would take for the Earth to tidal lock to the Sun.
For a smaller star like Proxima Centauri at 0.12 solar masses and a habitable zone distance of 0.032AU, the tidal locking would take 1/13,000,000 of the time.
Red dwarfs also have spend a longer period in their pre-main sequence stage (a billion years or so), Thus a planet would be subject to tidal braking for a long period before even being considered as hospitable.
So the odds are pretty high that a planet within the habitable zone of a typical red dwarf would be tidally locked.