UltraSonic sensor in rain?
will the buzzer make continuous sounds


If you mean the sensor will detect the rain drops in the air
Nop it's tiny to read it in the air
But if there is drops on the sensor your sensor will not gives you the right reading

There is a water proof ultrasonic sensors available.

I am working on water level devices, after long path of searching in different ultrasonic sensors and after I tried a lot of method like using water proof Cloth, I found the best way is using water proof sensors PLUS water proof cloth.

water proof sensors work perfectly in high humidity but at the same time if there is a water drop on the sensor the reading will be different, and for that some cars manufacturers used not only one sensor, to avoid the errors. and calculate the differences. 



The left car used old technology with separate sensors, but that's make errors the only good thing was to detect more things, in the next generation they mix them together.

water proof cloth will make the water drops not stuck at the sensor, but you will need to replace it every 5-6 months. "in your case because the sun will destroy the cloth" in my case and because my sensor inside tanks that's will least more.

I tried to spray the sensor with a different material to make my sensor not catch any water drops, it dose not work too. 

And to make my cheap sensor water proof, I tried to use ceramic layers, and that's not work too, they use it with ultrasonic fog maker, these layers not work with cheap ultrasonic sensors, it's need a lot of power to vibrate it and different frequency. and of course you need to replace the layers "depending on the environment"

If you find ultrasonic car sensor with special material for water drops just let me know, I am searching on that too.

NOTE These days car manufacturer use different ways, in the past the cover was vibrate itself and made from aluminum, now they cover it and make different filters to ignore the plastic cover, How?! maybe it's different plastic or material maybe they find away to vibrate the plastic! sorry I could not find the secret.