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If I stop an EC2 instance and then restart it (say, using the AWS CLI), its IP address changes. Is there any reason why `pulumi refresh` would *not* pick up the new IP address and update the stack output accordingly?

Note that I’m talking about _stopping_ the instance, not _terminating_ the instance. The instance ID remains constant/unchanged.

Refresh will update the state and I would expect the new IP to be noted. A `pulumi up` would then update the output.
You can use `pulumi up -r` to do both a refresh and an update.