I have the honda eu 2000 w/a companion and have the automotive charger cable. I haven't used it but believe it would be OK.
For an absolute positive opinion, I'd contact a Honda Generator dealer or the company for a response on the deep cycle battery charging.
2012 Fun Finder XT 276 Toy Hauler & Harley Davidson Ultra Classic with Condor wheel chock
2014 Dodge Ram 2500 AT 4X4 Crew Cab 6.4 L Hemi, 373 gears, tow package, Rambox option, Revolver X2 tonneau cover, Equal-I-zer anti-sway hitch.