No. The officer is supposed to give a 5th Amendment warning after he arrests you. Often, however, they do not. The only consequence is that the prosecution cannot use any of your answers to questions asked by the police after the arrest.

Of more consequence in most cases is the failure to advise you of the state's "implied consent" law - that is, your legal obligation to take a chemical test and the results if you refuse. This can affect the suspension of your license.