Routing an emergency call will use capacity wherever it can, even if it isn't capacity that belongs to your carrier.
Even if it means kicking someone off that is using another carrier.
It cuts through the multi-colored tape and just makes the call happen.
It won't magically produce good service where there is none at all. It doesn't pre-empt physics. It's not even a turbo-boost button.
But by being both largely carrier-agnostic and pre-emptive of other services, emergency calls can use whatever bandwidth might be floating around: Your own service might be such shit in a place that you'll never be able to make a regular call there, while an emergency call may find a better tower and work anyway.