My Sense is also outside the panel, way too crowded to fit inside and also makes connecting to a second generator panel easier. I don’t think there is any concern about unplugging and reconnecting different sensors to the main Sense box while everything is still powered, as long as you are not reaching inside the breaker panel.
The ammeter will work for sure, but it won’t broadcast to your phone. As long as you have internet and wifi with the generator Sense is more convenient since you can monitor generator load with your phone. I used to have an efergy system that I used exactly as you noted, to monitor power consumption with the generator. I would swap the probes when I powered up the generator, It had a small battery LCD display that sat on the kitchen counter that would show power. efergy was all battery powered so it worked just fine during a power outage.