No. Your tanks will not rust more/faster as a result of tumbling. Tumbling will leave them bare metal, and that's the best thing for them.
In the early days, manufacturers (USD especially) tried to come up with anti-rust coatings, using various plastic and epoxy coatings inside. None worked. They'd crack or pinhole, and water would get trapped underneath, concentrating, in effect, all the rusting action in one place. It was found that if the entire tank was left bare metal, any rust would occur over the whole surface, with negilible effects in any one place. Flash rust - light rust over large areas - is inesthetic but not very harmful to the tank. If there's water puddling in the tank, and the tanks are left in the same position for long periods of time, all bets are off, since deep pits can develop where the water is.
This sort of answers your second question too: no there is no coating or treatment that will prevent rusting, and you don't really need one anyhow if your tanks are being filled with dry air meeting accepted SCUBA standards. Every once in a while some idiot posts about spraying WD40 inside, but please don't. I would look into where you've been getting your air, as it is necessary to remove most of the moisture in order for the filters to function correctly, and wet air is often a sing of other, much more serious, air quality problems.