Ok, I have more information.
Firstly, there's no harm done in playing Naval Battles in a Group Format. You can only gain Oil. The picture linked above does show a negative number on a "loss", but that's in a 1 vs 1 competition which is not a Group Competition.
I was able to find the reward structure for the Battles section of the Naval Battle (ie: Activating the thing and doing battles to gain Stars).
So, in this above instance, you are:
A) Gaining Oil from participating in the Preparation Phase. Up to 800 Oil, as well as Bonus Attempts during the weekend for a more active clan.
B) Gaining Oil for Stars won during the Weekend section of time
and
C) Gaining a minimum of 300 Oil just for participating, even if you were last. Or more should you place somewhere in the middle of the Group so that the end reward is higher.
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All in all, there's nothing to be lost by turning on your Naval Battles and playing some games~