Yes, it does. Once the oxygen is consumed the reaction will stop. I recollect doing a paper napkin calculation (I forget what battery size) and concluded the volume of air consumed in it’s life was roughly the volume in a coffee cup. I would expect the oxygen trapped once you tape is back up is consumed in a matter of hours.
From what I’ve read on this topic the expected results of doing this will be mixed. The app note did not detail why but alluded to temp and humidity being factors. My personal experience has been good, the aid I use skiing has a 312 where I can get >2 months out of a battery using it twice a week and taping it between uses.