It's more a question of Ivy eligibility than NCAA eligibility. They can't graduate and stay at Cornell, so the question is how much time off did they take, and how much more are they willing to take?
Yianni, Vito, and Max did not enroll while in their two years off, as you suggested. It's not clear if all of Foca/Ramirez/Cardenas/Fernandes took those years off, but after this weekend, I'll bet they want to use as much of their NCAA eligibility as possible (two years each) at Cornell. Which means a bunch of fall semesters not enrolled.
(On the Hawkeye forum (aka the "cesspool" for good reason), some were thinking that Vito will have graduated and not be able to compete for Cornell next year, and if it were possible to get him at Iowa next year. Yeah, fat chance. I disabused them of that fantasy)