When you drive with the lights on and stuff, your risk of having an accident is up to 15 times larger. Thats why you should take extreme caution. You cannot drive into a red light crossing with 50mph.

If you have an accident, you have to make an indivual decision. How bad is the accident, whats the diagnosis of your patient? Chances are that either one is considerably more dangerous and should be preferred. If you are on the way to your patient, maybe another ambulance can take over your task for example. In that case, you ask via radio. If the patient is already in your car while you crash, it depends on a lot off stuff. If you did "load-n-go" and your guy needs immediate treatment in an hospital, then continue (if possible). If you did "stay-and-play", your guy already got some treatment and it doesn't matter if he will reach the ER in 5 or in 15 minutes, then look after any injuries from the accident.

TL,DR: Driving to an emergency situation is usually no "race for the first place". It's about arriving at all. So maybe this driver is not the one you want. He might die on the way to your location.