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Any time you make a surface less smooth it reduces the tendency to reflect sounds. It is very obvious in commercial settings. Head into a modern Chipotle where they often have an exposed steel ceiling and you'll be deafened compared to being in a similar sized fast food place that has an acoustical tile ceiling.
Of course the fact is that your home typically has carpeting , furniture, and drapery that all help reduce the echo effect. As far true "sound proofing" no popcorn ceiling is really built up enough to make more than a tiny difference. Even if you had a HUGE volume ceiling the popcorn layer is insignificant compared to the total construction technique / material choice.
Is it appreciable? No. Would it be noticeable to the human ear? Probably not; except an exceptionally "talented" audiophile.
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