We regularly set up, with jacks down and slides out prior to plugging in the power cord. This is no different than dry camping with just batteries. The system is designed to operate on 12 volts, and as long as the breaker isn't constantly tripping and resetting, your hydraulics will continue to work. The more the breaker trips, the weaker it gets, regardless of whether the AC is turned on. The instructions from Lippert says the system must be operated with fully charged batteries or with AC connected, but in any case you must have 12 volts from the batteries, and if you are operating the system with weak or partially charged batteries, you risk burning up the pump motor due to low voltage. If you look at the fluid recommendations, standard ATF has a pour point at least lower than -45 degrees, so unless you are in seriously extreme cold temps, the normal ATF should work. On page 16 of the manual, in the parts list, Lippert shows an 80 amp breaker, so anything less is not within Lippert's specs.
https://www.lci1.com/assets/content/...r_s_Manual.pdf