Q. What is the Redeploy Me Now Azure feature?
A. Today during the maintenance events that require host reboots the services on those hosts are paused very briefly during the reboot then resumed. While notice of the maintenance window is given in advance there is no control over the actual window. Note that for VMs in an Availability Set where there are multiple instances of the services spread over multiple update domains there is no interruption to the availability of the service but this would impact single VM deployments.
Newly announced at Build 2017 is the ability to choose a deployment time of your choosing within a 30-day window which will work by shutting down and moving the VM to an already patched host at your selected time. Note the downtime of the VM would be longer than the normal pause caused by maintenance since the VM now has to shutdown and start on a different node but it would be within your selected timeframe.