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

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!

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

An ROTC cadet is a weird standing when it comes to where you fit in. Check with your chain of command. Pretty sure it wouldn’t be an issue if you’re in different units. The fraternization only really comes into play when you’re in the same chain of command

I totally agree with LTC Jason Mackay, read into AR 600-20. It is very specific when it come to answering your question. Take it as Professional Development / Mentorship.

By regulation Senior or Contracted Cadets are considered to hold rank, generally for UCMJ, between E9 and WO1. Therefore, best case it would be fraternization between an NCO and a junior enlisted. Worst case fraternization between an officer and junior enlisted. While it's unlikely to be punished, it could reflect poorly and i would advise against it. Regardless, both parties should speak with their chain of command for advice.

Is the E4 active or reserve?

Probably not allowed. Look at AR 600-20, paragraph 4-14c(2)(b) - In relationships where one of the
enlisted members has entered into a program intended to result in a change in his or her status from enlisted to officer or junior enlisted Soldier to NCO, the couple must terminate the relationship permanently or marry within one year of the date of the appointment or the change in status occurs.
Perhaps leadership reads this a different way and says "Well, the Cadet is special, and not enlisted or officer, therefore..." However, at the end of the program and the Cadet is commissioned, the relationship falls under the strictly prohibited category between officer and enlisted. The "different unit rule" issue is a little misunderstood and has limited application. It does not apply here because the relationship falls under a strictly prohibited category. (See paragraph 4-14c(2)). Hope this helps.