Technically yes but will Telecharge discloses such personal information to the theatre? I don't think a theatre gets such info automatically.
I would be surprised if Telecharge didn't already automatically disclose the customers personal information to the theater. Technically the customer information belongs to the theatre. The theatre would definitely want to have that information for marketing purposes (demographics, etc.).
I know for a fact that personal customer data is automatically available to theatres that use Ticketmaster. It's a huge component of the service that Ticketmaster provides to the venue. (But Ticketmaster does not provide data to a theatre from a competing theatre's database of course.)