You’d really need to have current / voltage probes to tell where the fault lies. In a shop with resources to order test parts, you’d still try a second battery before doing a logic board swap if you don’t have the tools or skills or documentation to diagnose the precise voltage levels in and out of the power transformer(s) that are driven by the battery.
You don't need to disconnect the battery, but it's a good idea.
The only reason you disconnect they battery is to ensure that there is no power on any of the circuits which could inadvertently be shorted.
If people fry their logic board while disconnecting the battery, it's most likely they used a metallic tool (like a screw driver) to pry up the battery connector; use a plastic spudger tool.
Best Answer
Sometimes it helps to look at the replacement part to see what connectors it has.
From this picture, we can see that there is a PCB and a small connector cable at the top of the assembly.
This would correspond to this part in your photo
Disconnect that, and your SMC should reset.