This is actually untrue. The way they get to the hospital has nothing do with it, everyone is given a score upon arrival according to their symptoms, and are seen accordingly. Someone who was driven in with asthma symptoms would be seen long before someone brought in by ambulance with a broken leg. It sometimes appears that people who are brought in by ambulance see dr's quickly but in reality, they wait just as long as people in the waiting room, they just wait more comfortably.
Yep. I've arrived at the ED both ways with a similar set of problems both times & waited the same amount of time. At the hospy I went to, there is a bay where they park the stretchers, so you can't see them from the regular waiting room, which is usually 75% full of people who probably don't need to be there. But one time I arrived by car for something potentially serious, and i was triaged into a private room (they had no bays available at the time) and seen by the head of the ER in about 2-3 minutes of arriving.

Where I think it might make a difference is in a situation where the person might not know what to say to the triage nurse to communicate the severity of their symptoms. But in an ambulance, the ambos assess some of that and that info informs the triage score.