If you use semi dilute nitric acid it should not be too much of a problem. But if you use concentrated nitric acid for long periods of time or even semi dilute but with heat you can have serious problems. It depends on a lot on the stainless steel type, and what other ions are in solution (so depending on what you might be cleaning off, etc). Sometimes even dilute cold conditions CAN have a serious effect.
Honestly, I find that the best way to clean stainless steel is to take some finely powdered alumina (very cheap) and put very little water on it and make a paste, and then just use it and a thick paper towel or so and scrub it off. This is really just a polishing technique, but works better then anything I have ever found. And I clean a lot of stainless steel. There is more manual labor involved though.
On a large scale, just a polishing wheel on the end of a drill with the paste might be high throughput enough.