I've shot a few deer with suppressed .22 Magnums while doing urban herd reduction work and they all died, but not all instantly even with short range standing head shots. Based on that experience, I wouldn't feel comfortable shooting deer with any currently offered rimfire cartridge/bullet combination unless it was a survival situation and then anything goes.
That said, since you're going to be shooting antlerless deer in a place with lots of deer and a liberal bag limit, if you happen to shoot one and can't recover it, it isn't the end of the world as no protein goes to waste on the forest floor.
