IMO, yes. If the starter batt is out while you get a new one for instance, your house 12v things will still work if the house batt has a frame ground too.
Usually, you get alternator charging to the house batt with the engine on and that relay on the positive path closed, while the neg path is via the frame where both batts are frame grounded. In your case there is a wire for the neg path. Having that wire and the frame in parallel would reduce the R on that path and so for the circuit, and will give you more charging amps if the alternator can do any more.
1. 1991 Oakland 28DB Class C
on Ford E350-460-7.5 Gas EFI
Photo in Profile
2. 1991 Bighorn 9.5ft Truck Camper on 2003 Chev 2500HD 6.0 Gas
See Profile for Electronic set-ups for 1. and 2.