Yes.
(but the controller will know the transponder reports flight level).
Mode S has added nothing knew in this regard, what is knew is your callsign is also transmitted (probably so they can charge you for use of the air in due course or more easily prosecute you when you infringe controlled airspace). Of course the good news is I have yet to find a single unit in the UK with mode S capability and I have also seen the view expressed that if (when) we all have mode S the functionality will be turned off by controllers to prevent radar clutter. Ah well I know there was a good reason for fitting one
