Hello @EmmaLaine
No, with the GA travelcard you pay only the subscription charges and don't have to pay extra. The only exception is with some partner mountain railroads where you only get a discount or if you wish to change class to 1st class (with 2nd class subscription). For more information on where the GA is valid, see the area of validity of the GA subscription. Click here and open the PDF "Area of validity" in the downloads.
I wish you a nice day.
Kind regards, VlaznimA.