I don't see a reason why you couldn't interface to a Bluetooth LE device like a joystick - it should pretty much just be a matter of subscribing to notifications on the right characteristic.
The issue I've had has actually been finding something that really is Bluetooth LE - I did order a joystick a while back to try, but it turned out it was legacy bluetooth :(
something like this: https://play.google.com/store/apps/details?id=iyok.com.blejoystick&hl=en_US&gl=US
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