Hi alpharalpha,
Latex can oxidize faster with exposure to air and ozone and ultraviolet light along with other substances that can damage it ( see here for a latex compatibility chart ) and it’s generally a good idea for latex to have a suitable dedicated cover to give it the best possible protection and to help maximize it’s useful lifetime. It can also help protect it with handling. There is more in post #3 here and post #3 here that will give you some sense of the effect of different types of covers on latex and oxidation. Polyurethane foam will also discolour and can crumble with exposure to ozone over time.
I personally wouldn’t have as much of a concern with very infrequent use of an ozone generator, especially the newer ones which run for just a few hours, as long as your latex was well covered.
Phoenix