If I run out of AdBlue will the engine shut down

No, the engine will not shut down, but some engines automatically limit engine performance when AdBlue® supplies are depleted.

If your engine is equipped with SCR technology, your vehicle will lose power, and reduce its emission according to legal standards. The vehicle’s performance will be restored when AdBlue® levels are up again.
Note: Some engines will not start after you have run out of AdBlue®. Make sure that you have an emergency supply on board, or continue to the next distribution point without shutting down your engine.