Yes you should.
The fuse is there to protect your wiring. 2 battleborns, for example, can sustain 400A discharge for 30seconds. That's great, unless you tried to do that with factory wiring, in which case you'd cause a fire
6AWG is the house wire size for 12v
house systems and there is a 4AWG for the factory 1000w inverter.
6AWG is rated at 85amps for a 16ft run and 4AWG is rated at 125amps for a 16ft run. Technically you should fuse both independently. I believe the inverter already has a fuse inline (if Airstream wired per code
)- so you can just connect that to the battery directly and throw am 85amp fuse on the house line to the bus bar...