Is a relationship between an ROTC cadet and an E-4 in different units allowed? What is the rule with fraternization for ROTC cadets?

AR 600-20 and DA PAM 600-35 are your resources. Think you need to figure this out before the Cadet is Commissioned.

Using LtCol Mackay's references I say this:

2–27. Officer and enlisted (promotion into noncompliance)
a. Situation. SSG Rogers and SGT Thomas have been dating for some time. SGT Thomas is selected for OCS. May SSG Rogers and SGT Thomas continue their dating relationship?
b. Explanation. Generally, dating relationships between officers and enlisted are prohibited by AR 600–20. Prior to the date of commissioning, SSG Rogers and SGT Thomas must terminate their dating relationship. Alternatively, if SSG Rogers and SGT Thomas marry before commissioning, their relationship may continue after commissioning. The policy prohibiting social relationships between officer and enlisted personnel will not affect any married couple where one or both of the parties wishes to subsequently advance their military career. So, for example, AR 600–20 would also allow a civilian spouse of an enlisted Soldier to become an officer, or a civilian spouse of an officer to enlist.

I disagree with those who have opined that it shouldn't be an issue if you are in different units, but, if memory serves me, your cadet will only be commissioned if he successfully completes his degree program. But that's another problem!

Relationship in different units should not be an issue, but check with chain-of-command. Side note: I knew of some Army ROTC cadets who were dating and later married Air Force NCOs.

https://www.army.mil/article/138222/army_updates_reg_defining_inappropriate_relationships