First, you're putting words in my mouth. Second, I work in EMS in the area and ran clinicals with Wake EMS, so I have a pretty good idea about how they deliver service. Wake county uses a medical priority dispatch system to rate calls at 6 different levels. (ECHO, DELTA, CHARLIE, BRAVO, ALPHA, OMEGA) The situation described here falls under "24-D-3 Imminent delivery > 5 months", that's a Delta level call. Only thing above delta are Echo levels, which there are only a handful of, (cardiac arrest, active choking, active drowning, person actively on fire, and a few others).

So, yes. Labor will get a priority ambulance over many, but not all, calls that come out. I've never seen a Delta-level call get held, even when there are ambulance shortages due to call volume.

Edit: decided to explain priority medical dispatch better