More likely DFNewb is referring to fleets losing training when transferred among different commands. If the combat fleet joins the supply ship fleet, instead of the other way around, they can take a big hit to fleet training for "changing commanders" -- and another big hit for changing back.
By combat readiness I meant deployment time specifically. Ships can't fight in overhaul AFAIK and AFAIK there is no way to cancel overhaul once it starts.
You need to overhaul when using a training admin. Using a Naval or General admin does not require overhauling and while the training seems to be about half the speed I don't have to worry about splitting up my training fleets to ensure there is atleast 1 ready at any time, or constantly micro'ing overhauls.
Slightly unrelated but I notice there seems to be both Crew training and fleet training, what is the difference? All I know is the training per ship is there some sort of fleet training score I am missing?