If I move and update my address with USCIS, will this delay any of the processing times?

Usually not, but if the applicant moves to a new USCIS field office jurisdiction (such as to a different state), they will be subject to that field office's processing times, which could be longer (but sometimes shorter, too). In general, changing addresses within the same field office region won't affect processing times. Forgetting to update USCIS when an address changes will, however, cause delays.