PD power adapter can surely be used to power the router.

The only problems is that, as @elorimer said, PD is designed to charge batteries faster. So it will talk with the device (e.g. phone) to find out the correct output. This will cause short power cut. While this is not a problem of batteries, it could cause the router reboot.

So PD power adapter be used to power the router, but it may cut power sometimes causing the router reboot.

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