AFAIK, no, NOAA/NWS only has broadcast stations and no streaming capability or weather radio app. They do have two apps: mobile forecast and Ping for precipitation reporting.
WeatherUnderground offers the WunderRadio app for iPhone (a paid app) that allows playing of the streams submitted to Wunderground. The streaming does result in about a 1 minute delay from 'real time' broadcasts I've found.
Best regards,
Ken