You could absolutely say that the summation of all the frequencies a driver produces is also a soundwave. It would just be irregular and ever changing.

And a driver is far more capable than a single instrument seeing as it could reproduce an entire orchestra, choir and band's worth of sounds all at once. The sound it is producing is a summation of all the sounds it is producing and our experience of listening to it is definitely better described as multiple sounds as your brain can easily pick apart a violin and a drum playing and the same time.