In fact, it has been proven that deaf or hearing impaired people are better drivers, with fewer accidents or mishaps.
I am deaf myself (I have about 20% of "normal" hearing and I have been that way since I was born). Yes, I can hear sirens. They are very loud and high pitched. I can't hear them as loudly as a normal person can but I can hear them. As for the flashing lights, those are easily seen.
I use my other senses when I drive. I'm much more visibly aware of what is going on around me. In fact, how can all those idiots with blasting stereos hear a siren or horn? I can probably hear it before they do. Also, the sense of touch is very helpful...I can feel vibrations that people with normal hearing can't.
No, a hearing test is not required. The only restriction on my license is that the vehicle I drive must have right and left side mirrors. Since all cars have those anyway, that is not a problem.
I also drive an ambulance. I don't have any problem.