It actually would not be a Proth number. For a generalized Proth number k*b^n + 1 (or Thorp, k*b^n-1), the requirement is that k < b^n. For the rearrangement you provided, where k = b^(n-m)-1, it will not necessarily be true that k < b^m (such as when n-m > m)
Edit: Concerning your original question, programs usually have a limit on the size of k that are acceptable to test. With a different form, you don't have to fight with the k requirement.