depends on how much current the battery is sinking in an attempt to charge
when you have the Nav connected to a laptop, the Nav is not using much current as it is not powering the screen with updates and processing the data from memory and the GPS satellites.
On the road, the Nav is doing all these tasks and trying to charge the battery from a 5V/2A supply in the cradle. If the battery sinks a lot of that 2A as it has a low impedance then the Nav might struggle.
All you can do is try it on a local ride. If it does not work, try disconnecting the battery.