I'd say the answer is yes, because our ears cannot respond to anything faster than a frequency, or tone, of about 20kHz-ish. That is kind of like sampling rate, in some regard. And then there is only so much information, so many different sounds) you can pack into a roughly 20kHz bandwidth (there's an awful lot here to unpack, and I've not done it well), which is similar in some sense to bit depth, if you give some latitude for pushing a digital domain onto an analogue system. If fact, because of that bit depth, or packing information into how fast we can hear, most of what we listen to sits in the 50Hz to about 8kHz range. It's mostly music that routinely takes us to our limit. Lots of noise will do it to.

Fundamentally, we can't hear sounds that have tones that are too high pitched, and we can't resolve separate sounds that are too close together, even if they're in our hearing range individually. So it's kind of like eyes, but our ears are much faster than our eyes, largely because they're much simpler.

Last thing, I've ignored amplitude, or loudness. Others have explained it well. If sounds are loud they can reduce your effective bandwidth at any given moment. So information (sound) in a loud place can get lost even if you could otherwise hear them.