Three answers to the "Is a house battery necessary"
On a trailer YES!!!, DO NOT TOW WITHOUT A PROPERLY CHARGED HOUSE BATTERY
(why: well you see, it is that battery that engages the EMERGENCY brakes on the trailer if trailer and tractor (tow vehicle) part company at an unfortunate time).
On a rig with selected converters such as the Magnetek 6300 line YES, dang convrter needs an upgrade but then (if trailer does NOT have electric brakes) you can do away with it, but till you upgrade, YES you need a battery.
Note: When I said "RIG" I meant motor home OR trailer.
On a motor home with a decent well filtered converter such as a Progressive Dynamics 9100 (or better yet 9200 or 9100+wizard).. Optional.
