It depends on the source of the yeast. Wild strains of yeast sometimes produce methanol (bad) as well as ethanol (good) and lactic acid (neutral but sour). Brewer's yeast has been selectively bred to optimize ethanol production.

Even with brewer's yeast, if the fermentation is followed by a distillation process, there are generally steps to remove any methanol that found its way into the fermentation process (for example, because cellulose was in the stuff being fermented, and fermentation of cellulose produces methanol). That's why the foreshots (first distillation products with lower boiling temperature) are discarded.