It really depends. There are alumni only professional internships (which require you to have participated in the CP). However, for all other PIs, my experience has been that they are looking for the best candidate who fulfills the job description. Therefore, CP or Disney experience is NOT required. (In fact my experience was that most non-alumni positions were NOT filled by individuals who had worked for the company).
However, in some cases it helps to know the hiring manager (or a member of the team) and there someone with Disney experience my have an advantage.
Hope this helps!