Currently when pushing updates via our CI/CD pipeline to the Azure Web Apps the nodes are being forcefully rebooted by azure once the configuration changes are completed.
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If downtime is your concern, it looks like MS starts up another container when you hit Save in the application settings blade, and then transfers all new requests over to the new container. The old container is given 2 min to complete all requests, and is then shut down.
https://social.msdn.microsoft.com/Forums/azure/en-US/f15b207b-c063-46e5-b87a-2b157641c8c4/does-changing-an-app-setting-and-saving-restart-the-app?forum=windowsazurewebsitespreview
I tested this on a Web App by repeatedly hitting an endpoint for 30 seconds while I changed an application setting and hit save. I saw the application start, but did not see any timeouts, only 200 OKs. FYI my web app only used a single slot.