Like Don, I don't remove my batteries any more, although I used to when they were just 12v deep cycle ones instead of golf cart types. They stay charged by the solar panels even without shore power, but the trailer stays plugged in anyway.
As to being able to move the slides without them, I've done that many times on both our current Montana and our TT before it. I'd bet your Carriage has an 80 amp converter and should be able to do it as well.
'06 F350 TD, Softopper, airbags, AeroShield, coolant filter
'10 3665RE Hickory edition, wetbolts, Firestone LTs, Trimetric Battery Monitor, 4x100w panels & Morningstar TS-45, still tweeking.