If an NCOIC is getting court martialed for violating the UCMJ, can they remain in that leadership position until the court martial is over?

The NCOIC is still an NCO with a job until their trial is complete. The position they hold at the time is based on the discretion of the commander. Depending on the nature of the charges, and the nature of the person's position, the commander they move them or leave them in place.
Until a person is convicted they are simply accusations and if the accusations are not serious enough to warrant confinement, then you can't simply remove people from their job without any justification.
So, good answer to your question, it depends

Persons undergoing Court Martial proceedings are usually suspended from leadership positions (never knew anyone not to be) until the investigation or proceedings are completed. Look up AR 600-20 and it discusses these issues.

I would think that if that violation or accusation occurred while in that leadership position and affected office personnel or his platoon. section or company it would be better to move him to another assignment until the courts martial proceedings were completed. That way unit cohesiveness, morale and team spirit wouldn't be adversely affected. Just my opinion without looking it up in the AR 600-20 Army Command Policies and Procedures