well, yes, but you will have a viable claim for false arrest if your behavior bears no resemblence whatever to the statutory prohibition. That will deter the police from indulging in personal frolics (ie, a disturbing the peace arrest where there is no prior request for compliance, eg. to arrest Sheehan w/out asking her to cover up the t-shirt.)
In the case of harassment as a vague term potentially but not necessarily embracing pure speech, you leave the cop with too much discretion, and expose the speaker to the detriments discussed above.