Rain drops keep fallin' in my car....

For sure, if you just crack the window a 1/2" or so, they should stop water coming in. Have had them on a previous car, but I wouldn't do it again though. They're plastic, tend to look burnished after a while. On the car we had them some cutting of weather strip was needed, not sure with the Prius though. Over time they can start to get loose. Also makes it a little harder to clean the glass, but not a lot.

I'd be inclined to keep it stock, exercise caution after heavy rain.

 

Yes they would. I had the visors on my 2008 Prius for years and they never gave me any problems. I installed them on my 2016 and love the convenience of rolling the windows down a bit and not getting the big air flow into the cabin.
We don't get a lot of rain in Southern California, but when we do the visors do mitigate the water entering the cabin.
Just get good quality and pay attention to the installation instructions. The JDM and Wellvisors do not require any installation modifications on the Prius. I would recommend either of those two brands.

 

Sure, if installed correctly they should.

I personally don't like the look.
And since Toyota spent a LOT of time in the wind tunnel designing the body shape, I hesitate to throw aerodynamics off by taping ledges to my windows.
But many people like them, and the utility benefit they can provide.

My Old Honda Fit seemed designed to dump water on your lap if it was raining.
I lived with it.
Kept me alert.

My Gen 3 Prius is a lot better in this regard.