Probably not because you have a set of rights associated with the login, assigned by specific administrators rather than at a top level ie BRS don't manage your rights and assign your privileges to each club; the clubs manage them.
However, this is based on a logical approach only...so could well be wrong in real life!
I don't use the phone app but my understanding of the PC version is that you can book times at any course using the software, either as a Member of or a visitor to a club
If you are a member at more than one club, each club will arrange an individual logon for you.