It depends on what your goal is. But in most cases, I'd say no. If the goal has anything to do with understanding real language written by real humans, it's better for the system to be able to handle texts with errors.

True, but having some noise in the label is actually good for generalization. If it's only learned on perfectly correct sentences then its tolerance for mistakes will be very low.

Maybe the examples for a language test should use language that people actually use every day.