Sure, most people aren't as it isn't advertised anywhere. The Mission Commander's have the option to have a Cadet as an XO for their CULP mission. I don't think there is any certain requirement as far as what MS level can hold the position, though all of the one's I talked to at Knox were all LDAC grads and had completed MS4 year. Most were completion cadets that had a semester or two left in school and were asked by cadre members from their school to come along as an XO. There really isn't anything set on what the position entails as it all depends on how the MC utilizes the person, but they aren't tied to a specific CULP team and will usually spend the entire length of the CULP mission for that country in-country. I was an XO this past summer and spent roughly 3 months in-country. I tagged along with the different teams on some days (there were 4 over the time I was there) and did some of the stuff they did, but I also spent a lot of time working at the embassy working on contracts for our drivers, hotels, and various other things that the teams needed. Do to the security restrictions of the embassy for the country we were in, every time the teams were interested in traveling around the country on various excursions, I made sure the itinerary's and security stuff was taken care of through the regional security officer at the embassy. I also did a bunch of other boring stuff prior to the actual start of the mission tracking the status of each cadet on each team and making sure they had everything completed so that they could go. I was also a part-time tour guide for the new teams when they arrived in country.
I don't think that anybody that's done this has the same experience as any of the other XO's, but it was a neat opportunity and I got to learn quite a bit about working with host-nation assets and various agencies at an embassy. And traveling abroad for 3 months isn't something many people get to do in ROTC.
Once again, I don't know if there is a way to "apply" for this position as I was asked by a cadre member at my school and he had people at Knox pull my name into the position. The others I talked to at Knox were also traveling with cadre members from their schools.