So, how does the latest iOS 11.3 public beta handle an iPhone crashing due to a worn battery? Well, I happen to have an iPhone in the lab that is awaiting a battery replacement, and after stress testing it for a few hours I managed to cause a crash.
On restarting, you will see a notification informing you that This iPhone has experienced an unexpected shutdown. Heading over to Settings > Battery will show you this screen:
Clicking on that Disable… link brings up the following:
Choosing to disable performance throttling cannot be undone, although the throttling will be re-enabled if the device crashes again.