In principle, it would, if the temperature of the Universe were absolute zero. A black hole of stellar or larger mass radiates Hawking Radiation at a far lower bolometric temperature than that. Hence, rather than losing mass, a black hole actually gains mass as the warmer cosmic background radiation falls into the black hole. This means that the equilibrium direction is for black holes to grow as a result of exchange of thermal radiation with their surroundings, at least until the Universe is billions of time as old as it is today and the cosmic thermal radiation temperature has dropped to VERY close to absolute zero. In short, Hawking Radiation does not cause a black hole to evaporate in any reasonable period of time.