Pretty sure that for any sort of school (and CULP) you need to be contracted.
You are correct- Airborne, Air Assault, CULP, all require to be cadet be contracted. Believe same for all the other Cadet Practical Field Trainings- Mountain Warfare, Northern Warfare, Cadet Field Training at USMA, SF Combat Diver Qualification Course, Cadet Leadership Development (Infantry) WHINSEC.
CIET, as of now, does
not require cadets to be contracted. Which makes sense. Cadet Command plan is commencing 2016 every AROTC cadet who does not have enlisted basic, will need to attend CIET. If CC limits only to contracted then every 3 year AD or campus based scholarship, plus sophomore non-contracted, would have to go between sophomore and junior year, because they have CLC b/t junior and senior summer. Freeing up sophomore-junior summer allows contracted cadets to apply for CULP, and other cadet field training.
https://www.armyrotc.msstate.edu/training-opportunities/ has a good synopsis of available programs.
"Generally, in a typical year, the total number of CPFT allocations equals approximately ten percent of the cadet population at large. Battalion commanders will prepare, select and send to CPDT only those with the highest potential for completing the CPDT training and for being commissioned. Cadet Command pays for travel. Billeting and mess are provided by the installation in most cases. All cadets must meet the eligibility criteria to be selected."
MSIIIs also have additional opportunities:
Cadet Troop Leader Training (CTLT) track provides Cadets the opportunity to experience leadership in Army Table of Organization and Equipment (TO&E) units over a three to four week period. Cadets serve in lieutenant-level leadership positions in active-duty units.
Drill Cadet Leadership Training (DCLT) track four-week provides Cadets the opportunity to serve in a platoon leader or executive officer positions.
CTLT Internships opportunity to exercise specialized language, technical or research skills. Internships range from three to eight weeks long and can be conducted before or after the required CLC.