Yes, but both Bakka lists in history functioned under the Big Gun Lobby and both had carriers so I figured that some carriers were acceptable.
The level I was thinking was for the Big Gun fleet, only Dominion and Rath/Dominus Astra if they pay for it. The rest can only be through reserves.
Gareox fleet might be Emperor, Despoiler, Oberon, Despoiler, Exorcist, Mars, Dominion, Jovian, Dictator, Lunar (because of how common), Defiant, Enforcer, Bakka escorts.