What happens when an ambulance is going to whatever emergency but...?

Protocol varies by area. Realistically, it would depend on the situation. Chances are If the accident is bad enough to warrant immediate life saving needs then the person is likely going to require extrication from the vehicle. I don't carry extrication equipment on my ambulance.

The law says once we are dispatched to a call, we have a legal obligation to our patient. In most cases we will call the accident in, notify persons that help is on the way and continue to our original call.

Another factor to consider is does the accident pose a safety risk to our response (i.e. is it blocking our path). If so, then we will commit to the accident and call for other units to go to our original call.

If we have a patient on board, our hands are tied. We cannot abandon the patient to tend to accident victims - even if they require life saving care.

There is no set rule.

I'm an EMT as well and if it's a bad accident we will call a "still alarm" which is a incident that we came upon and we will stop and tell dispatch that they will need to send another unit to the previous call. As a EMT my obligation is life safety so to call it in and not stop would put more people in danger then need be. I have closed down roads inorder to protect the accident scene.