I used to believe it wasn't possible to make much improvement in any convertible. Then I had an opportunity to work on about a dozen Pontiac Solstice/Saturn Sky roadsters. I only worked on the first one with the understanding that I expected no improvement. The owner was desperate because his wife wouldn't get in the car after all of his performance mods.
We worked through the car and the result was stunning. 90 MPH on Route 95, top down and we could speak in just slightly raised voices. Top up and it was a nicely quiet car. One owner thought there was something wrong with his car after treatment - until he realized he was hearing the ticking of an analog alarm clock he had in a gym bag in the car.
This does not mean that every convertible can be made quiet. If the dominant noise with the top down is air turbulence, treating the car isn't going to help. If the dominant sounds with the top up are air turbulence and top noise, treatment won't help. If the car has decent aerodynamics, the convertible top was designed to be quiet and most of what you hear is engine, exhaust and tire/wheel noise, there's a good chance for a good outcome