It also depends on what -type- of hearing aids they are, and where you got them. Some hearing aids are just amplifiers with basic controls over treble and bass. Basically - fancy ear buds. Others are incredibly complex and dynamic, with multiple functionality to shift on the fly when you change environments.
Some of them have good noise reduction ability, some have zero noise reduction ability, and most fall somewhere inbetween. None of them have "full" noise reduction ability. If you can hear your wife, you'll hear that paper crinkling. But your wife's voice should be crisper, louder, and clearer than the sound of the paper.
UNLESS...unless it's not actually paper you're hearing. If you have ear hair, or if you put your aids in over hair that drapes over your ears, you might be hearing the sound of hair against your ears. Ask me how I know this