How to get Power into a Power over Ethernet cable?
Yes, you would connect 4/5 (blue/blue-white) both to VDC+, and 7/8 (brown/brown-white) both to VDC-. That's standard to the pinout for PoE. 

Ethernet cables use very thin gauge wire (23-24AWG). Doubling them up increases the amount of current you can safely put over the cable. 

Before you do that though, definitely look into how tolerant your input device will be to being directly connected to your boat's power system. Either your boat's power or the equipment would have to be carefully regulated. Otherwise, you could easily damage it by exposing the equipment to several volts above or below the target 12V between battery charge and discharge cycles. 

It's also worth noting that 12V is not common in PoE systems. Most operate around 46VDC. Can't speculate further without having the datasheet for your equipment. Either way, the power adapter they recommend is probably for very good reason. 

At the very least, you will want to put an inline fuse on the VDC+ side.