It does if OW dives are done as part of the Nitrox course. If only the classroom portion is done, then the diver can obtain the card & use Nitrox, but it can not be counted as one of the specialties used for AOW.
With SSI, OW dives MUST be made in order for the course to count towards the AOW cert. or any higher level. SSI changed that standard a year or so ago to prevent someone from obtaining a more advanced cert. by taking courses & not doing any dives (courses like Nitrox, Perfect Buoyancy, Equipment Techniques). If OW dives are made that incorporate the skills learned in the classroom &/or pool, then the specialty can count towards the more advanced levels.
My LDS gives the student the option of doing the dives or not. If dives are done, then yes, it can count towards AOW or higher, if not, then it can not.