Short answer is yes. It would be the primary source of the indicator coming on. Your indicator circuit is simple, no PCM involved on single gen solution. The positive side is tied to ignition circuit, the ground side is tied to the voltage regulator. The line is grounded when the alternator is not running. When the regulator/alternator becomes operational it releases the ground connection and the light goes off.
"Goldilocks" 2020 Ford Transit High Roof Extended 3.5 EcoBoost AWD Homebuilt