A newly released NCAA interpretation prohibits nonqualifiers from not just practicing or competing with the college team, but with any outside team, including a national team:
The committee confirmed that a nonqualifier is not permitted to practice or compete on an outside team, including a national team, during the academic year of residence, which includes practice or competition during an institution’s term-time official vacation periods (e.g., mid-term break, Labor Day weekend) and during the academic year between terms when classes are not in session (e.g., winter break).
This means that if a nonqualifier starts at a school, then receives a call-up to a national team, he or she would potentially be affecting their eligibility by accepting the call-up or even a tryout. It might be possible to get a waiver in the case of a national team call-up, but it would have to get by an interpretation that specifically mentions national teams.
The ban on outside teams generally is understandable, otherwise nonqualifiers could enroll at a four-year school and simply play on an outside team, which defeats the purpose of sitting out and might not even use a season of eligibility. But national team call-ups are so rare and in so many other places are considered special enough to rate an exception to normal NCAA policy, that another exception seems warranted here.