No. It's actually important for an effective digestion. Not just because smaller pieces are easier to break down, but because the enzymes in the saliva start the process.
Digestion is important but I think being able to breath is more important. Poor digestion won't kill you as readily as suffocation or pneumonia from aspiration. They, being protecting food from blocking or entering the trachea and digestion, both seem pretty important as part of the whole chewing system, so I don't think it's a plain "No". I should correct my original comment from mainly to one of the main reasons.
Chickens have no teeth, but they chew their food (the food is first stored in their crop, along with gravel, where it is "chewed" before passing to the stomach.)
