Done right you wouldn't be able to see it. Often in movies the filmmakers will add milk to the rainwater so it shows up on camera, which is probably where the "white lines" depiction of rain in games comes from in the first place.
I've heard of that trick, but I think the result is still quite far from the 100% opaque "plastic toothpick" look you see in some games. The milk/water ratio is probably not that high, resulting in a liquid that is at least more transparent than opaque.
Also, real rain can be quite visible in the air even if it is not
always so. It depends on rain quantity, drop size, lighting conditions, and whether the the background is light or dark. In daylight, you can usually see light rain against a dark background, and heavy rain against most backgrounds. Making the rain a bit more opaque than in real life means that you see it even in conditions where it would be invisible in reality, and I'm fine with that (and actually prefer it) as long as it's done in a subtle way. Among recent games, Ground Zeroes and Watch_Dogs did it well in my opinion (PS4 version if it matters). Infamous Second Son also had good rain, but as it was almost invisible in some lighting conditions, adding a little "milk" to it might have been preferable..