Absolutely! Ozone is produced as a byproduct but I don't have any refrences at hand. More generally it can be said reactive oxygen species are produced as an intermediary that turn into several compounds as plasma is cooled.

Whatever gas you make bubbles from is going to be ionised(plasma is created during cavitation) and it's going to produce a cocktail of chemicals inside as it cools below ionisation temperature.

Many of these are shortlived eg oxygen reacts with hydrogen or nitrogen to form more stable compounds but some intermediaries can be stable and be detected.

The absolute max amount of nitric acid you can get for example is proportional to the amount of air dissolved in water. If you cavitate entire 1L of water max HNo3 you can get is about 20mg. Realistically it's not possible to cavitate such a large volume of water at once and there's a competition among reactants to form other products eg oxygen is going to used for hydrogen peroxide as well. Very sensitive instruments are used to detect these.

This is studied in sonochemistry —using bubbles to drive chemical reactions.Not enough for large scale production but small doses of chemicals — mostly radicals can be delivered by bubbles making it useful as a disinfectant.