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Basically, yes. Our eyes capture the light that goes into them at 24 frames per second (please correct me if I goofed on that) and the image is upside down.
Our brains turn those images upright, and it also fills in the blanks. The brain basically guesses what's going on between the frames. It's highly adapt at pattern recognition and estimation.
My favorite example of this is our nose. Look at you nose. You can look down and see it a little, and you can close one eye and see more of it. It's right there in the bottom center of our view, but you don't see it at all everyday.
That's because it's always there, and your brain filters it out. The pattern of our nose being there doesn't change, so your brain just ignores it unless you want to intentionally see it. You can extrapolate that to everything else. Most things the brain expects to see, and does see through our eyes, is kind of ignored. It's there, but it's not as important as say, anything that's moving.
Also, and this is fun to think about, we don't even see everything. The color spectrum is far wider than what our eyes can recognize. There are animals, sea life and insects that can see much much more than we can.
But to answer more directly, you are right, the brain does crazy heavy lifting for all of our senses, not just sight. Our reality is confined to what our bodies can decifer from the world through our five senses.
We definitely are seeing things faster than 24 Hz, or we wouldn't be able to tell a difference in refresh rates above that.
Edit: I don't think we have a digital, on-off refresh rate of our vision, so fps doesn't exactly apply. Our brain does turn the ongoing stream of sensory data from our eyes into our vision "video", but compared to digital screen refresh rates, we can definitely tell a difference between 24 and say 60 fps.
Generally humans don't perceive a difference above 60 Hz.
It's noticeable, it's just not massive. My phone screen runs at 120hz but I don't notice a difference unless I'm scrolling rapidly. Gaming culture (driven by corporations) really overemphasizes its importance. Gamers as a group seem to be easily duped by impressive sounding numbers, just like the rest of the population.
Also keep in mind there likely isn't a lot of selective pressure on biological vision refresh rate, so I wouldn't be surprised if there's a fair amount of variability in the ability to discern a difference amongst individuals.
Finally, a reasonable reply to my comment.
It's a hot button topic for some people. I'm for the biological variation explanation - some people seem to really notice a difference while others don't.
I think what the people who get really upset notice is that they dropped a few extra $100s on what's often largely a marketing gimmick.