The ubiquity of M dwarfs, combined with the relative ease of detecting terrestrial-mass planets around them, has made them prime targets for finding and characterizing planets in the "Habitable Zone" (HZ). However, the Kepler mission finds that terrestrial-mass exoplanets are often born with voluminous H/He envelopes, comprising mass-fractions (M_env/M_core) >~ 1%. If these planets retain such envelopes over Gyr time-scales, they will not be "habitable" even within the HZ. Given the strong X-ray/UV fluxes of M dwarfs, we study whether sufficient envelope mass can be photoevaporated away for these planets to become habitable. We improve upon previous work by using hydrodynamic models that account for radiative cooling as well as the transition from hydrodynamic to ballistic escape. Adopting a template active M dwarf XUV spectrum, including stellar evolution, and considering both evaporation and thermal evolution, we show that: (1) the mass-loss is considerably lower than previous estimates that use an "energy-limited" formalism and ignore the transition to Jeans escape; and (2) if planets form with such bulky H/He envelopes, only those with very low-mass cores may eventually be habitable: cores >~ 1 M_earth, with >~ 1% natal H/He envelopes, will NOT be habitable in the HZ of M dwarfs in spite of photoevaporation. I will end with a discussion of the general implications for habitability around M dwarfs, and for the search for habitable M dwarf planets to be undertaken by upcoming missions such as TESS, CHEOPS and JWST.