"She's away until 2 days before payment is due."

Well at least she isn't away until two days after payment is due

Why don't you plan to take the classes, but if you want to be extra sure talk with her they day before the deadline. You could even ask the studio to have her call you about them. Or you could ask if you could register for the class on the understanding that your payment could be credited to private lessons instead if your teacher feels you do not belong in the class.

In actuality it's very rare to not a let a student sign up for the class after the supposed deadline if there is still room. What does happen sometimes though is if not enough students sign up they decide to cancel that class.