Yes, she would need to re-audition. Reason being... there are roles set aside specifically for CPs and there are roles for Seasonal. Even though they seem to be interchangeable, it's all based on head count (and it's no secret CPs are paid less).
So for a position in a CP role, she would have to audition - and will likely go through training again.
My very good friend did the CP 3 times as a Character Performer (remained Seasonal between all programs), and did the audition/training process 3 times. Now she's off to Japan, where she'll get trained again!
As for the Summer Alumni Program - only high need roles are available for this program (such as F&B, Custodial), Character Performer is not traditionally included.