Does the third "ACC" or accessory wire of this GPS need to be connected to 12V for it to charge?

Generally, ignitions have 4 positions: OFF, Accessory, Run, and Start.

Start cranks the engine. Run is for normal driving. Accessory is for sitting parked with the car off, except you want comfort/convenience accessories still working, such as the radio. It avoids running blower, wipers, rear defog, fuel pump, cooling fans etc. to avoid running down the battery.

"Hot in accessory" means the circuits are energized when the car is in Accessory or Run, and sometimes Start. Some circuits will shut off during Start (e.g. blower and wipers) because the battery needs all its power to start the engine.

You're missing what's going on. Orange isn't a signal. It's power.

The red line is "always hot" and is only there to keep memory alive (similar to the station presets and clock on a radio). It can't draw more than a couple of milliamperes, because it's always-on, and would drain the battery when the car is off and parked.

The orange wire actually powers the device. It is tapped into a "hot-in-accessory" line which is energized in accessory and run. It doesn't need its own fuse, because you typically just tap an existing circuit such as the radio circuit, and that will already have a fuse.