Nah. Fascism only tolerates one power, that being itself. It can emerge from either the state or corporate side, and necessarily subsumes or destroys the other, just as it subsumes or destroys unions, families, friend networks, communications, and anything else that can establish power. That doesn't mean the merger of two of them is the defining feature.

Fascism was corporative, but in Italian the word has a very different meaning compared to the English one.