Most likely YES... I would trace the WHITE CABLE just for kicks and make sure it does indeed go to the trailer frame ground which will not be very far away from the battery...
Be sure to properly CRIMP on the battery cable ring terminals... Using adhesive type heat shrink ends really does a nice job around the outside battery connection terminals... I am not a big fan of stripping back the battery cable and pushing into some sort of screw down type connection especially around the batteries. Professional crimp is what you want use here around the batteries.
I seem to do alot of battery cable work here on my OFF-ROAD POPUP and I finally got one of these 8-ton hand crimpers in a nice box with different size crimp heads. I use this all the time here...
Most all of my 12V DC connections incuding the battery use the ring terminals so I always have a good supply on hand. Ordered from AMAZON...
Also when you get your battery be sure to observe where the word 'NEG' or the symbol '-' is stamped on the battery case. This is where the frame ground cable goes to...
After you get all hooked up and running alot of folks will dab some RED finger nail polish on the POSITIVE cables or at least take a photo of on your cell phone to always have handy photo to look at...
Another thing I do sometimes is use color coded heat shrink ends. BLACK for Positive ends and White for Negative ends etc... I run into the automotive world with things in my OFF-ROAD POPUP where RED is for Positive and BLACK is for negative. Using the correct RV color for the wiring on the heat shrink ends really helps here sometimes haha...
The old Electrical guys turn over in their graves when one ends up putting a Red cable on top of a BLACK cable haha.... I have at least three places i know of of in my trailer wiring where this happens. Bought a new replacement JENSEN Car radio and it came with permanent wiring of RED(+) and Black(-) cables...
Roy Ken