Bear in mind that FirstNet is its own thing, to an extent. Internet providers will (almost?) always discard priority bits for *general public Internet service*. FirstNet doesn't qualify as a service for general use, so it is possible that some markings may be reacted to, or at least not discarded outright. That is a question for someone more knowledgeable on the FirstNet service directly.
What I can add is that in a previous life at a Tier 1, any traffic on a port that touched the public Internet in some manner had priority markings squashed, and that traffic was placed into the same priority queue on our backbone links (I recognize that the latter part of this statement opens up some other neutrality-adjacent worms) - this includes traffic accepted via peering, not just transit. Customers with private L2/3 services would either have their markings preserved or acted upon, depending on whether or not that service was "QoS enabled". The conclusions to reach here are, IMO:
1) Even if FirstNet itself responds to or accepts prioritization markings, destination networks beyond, where applicable, may not, so the relevance may be limited regardless.
2) This is deliberate choice at the provider level, even if that choice is effectively a consensus