No, FireConstraintType is the Entrenchment mechanism which dictates when an entity is allowed to use a weapon. Like Starbase upgrades. The basic SB starts with one weapon, and upgrading it unlocks the other two. Or the TEC's hangar bay starts with the autocannon weapon, but it has to be unlocked through research before it can fire.
Ardborne wants to do that but tie the weapon unlocks to capital ship levels (say a level 1 Kol might only be able to use its laser to start, in a few levels it can use laser and autocannon, and a few levels later still it can start using its beams). Stuff like that.
Unfortunately, there's no setting that I know of to make it dependent on cap ship level, only research and SB upgrade rank.