come on in, the water's fine
Sure, lots of small schools in USA would be happy to have somebody volunteer their time, and the FAA has no problem with free instruction.
SOME insurance companies might balk at insuring the aircraft because the school has no "control" over the "employee" so he might not adhere to safe practices. Underwriters are so unreasonably paranoid!
The terminology you're using makes it sound like a non-FAA environment, conceivably there might be a governmental difference in interpretation there.
I have the impression that the USA has rolled over to requiring the Commercial before the CFI, but it used to be that one could get a CFI in USA with just a Private Certificate.