Theoretically:
If one were to distill a beer at 172.3-211.9*F with the intention of throwing away the distillate, in order to produce non-(or low-)alcoholic beer, would the remaining beer contain enough viable yeast to carbonate bottles with the addition of priming sugar, or would additional yeast in low quantities be necessary for carbonation?
Secondary question (not necessary for the answer):
Should the yeast be of the same strain as the original yeast, or would a different kind be acceptable due to the fact that the beer has already been brewed and only carbonation is sought?