Hey (love the name) Jackie Brown,
As a manager, I would not allow this. What is learned as a personal trainer during certification is quite different than group fitness certification, though there of course is some overlap.
That said: “could” you? Yes. Since there is nothing regulating you can’t. But, if the client is injured and you aren’t insured as a PT, this could come back and bite hard. For example: You “could” do your own taxes. An accountant is a professional trained in this area and pertinent laws. I’d trust them more…
There’s nothing wrong with doing what is best for the client and getting yourself certified for the future, which is what I would suggest if you were my employee 🙂