On some guns they last a long time, like thousands and thousands of rounds. Other guns will eat the O-ring in a couple hundred rounds. I've not figured out why the difference is so large.
With 3.5" shells you likely won't know the o-ring is torn or gone, same for heavy 3" loads. It will start failing to cycle with lighter loads if the o-ring is damaged, and that will be your first indication. It won't hurt anything but reliability if the o-ring is damaged.
If I were you I would go down to the hardware store with the new o-ring and match it to one there. This way you pay about 40 cents each instead of $6 or so that Remington charges. The latest Remington rings I have seen look silver in color, some sort of metal impregnated rubber, and they don't last well at all. If you have a good hardware store or a hydraulics shop nearby see if they have viton o-rings. These typically are yellow in color and last better than anything else I have found.
Hope this helps.