I think they have a special ability (through the tech tree) that gives them assault bots, but I dont believe they can attack any other way.
They do actually have a peashooter gun that they can shoot with
But it's about as effective as the colony frigate's gun.
But yeah, light carriers definitely don't. It doesn't actually depend on whether the ship has a gun or not, IC made it so that support ships in a fleet ignore a direct attack order if your whole fleet is selected so they can focus on their support jobs (this is a change from lots of feedback during the beta, since it was a pain micromanaging Hoshikos because they can't cast and attack at the same time).
If you only have the support ships selected, then they will obey a direct attack order, obviously if they have guns 