Nope. I don't believe for one minute that anyone outside Nixon's little secret circle knew about that taping system. It was just too explosive, HUGE news when Butterfield spilled the beans in summer, 1973.
Most of Nixon's top aides didn't even know. They would never have said the stuff they did in the Oval Office if they'd known it was being taped. I mean, what's the use of a secret system that's not secret? The guy was paranoid.
Had the FBI known earlier, or even suspected, that there were tapes, there would have been subpoenas issued for them long before the fall of 1973.
Quite possibly you are correct, however there may have been others, such as a few top SS men who suspected it.