Your setup should work just fine. But keep in mind that the Application Gateway will have multiple instances and you need to check the health of each site before sending traffic to the Web Server. In that case, the number of probes per second on each VMSS instances will be high. Make sure that is not affecting the performance of the server.
Application Gateway also supports widlcard listener where multiple sites can be hosted with single rule and listener.
Regards,
Karthik Srinivas