Helicopters has multiple "car" entities used at different times to handle animation and collision (or lack of it when flying). I think that causes Autodrive to lose track of the vehicle. When the Helicopter appears to be doing nothing you might need to either re-select it with the remote control, or open the grid and and remove/replace a sensor, to trigger an event for Autodrive to detect the new unit_number.
Hovering the mouse over a nearby roboport should highlight a hidden chest under the Helicopter if it has successfully detected a logistics network. If you can't make this happen then I'd love to see your save file to debug it further.
AAI also exchanges car entities on the fly but it sends a custom event on_entity_replaced so that other mods can follow the changes. Helicopters doesn't do that -- I think, haven't had much time yet to look through its code.