I was recently working on a project in which we where using an Application Gateway with WAF to send traffic to certain destinations based on URL path.
During a conference call with the application developer and a Microsoft Cloud Solution Architect I was asked the question, what are you going to use to load balance the backend pools?
I initially responded the WAF as this is polling the backend pool to determine which VMs to send traffic to, so logically should include a Load Balancer, but hold on a minute I have never seen any settings for Load Balance rules. In comes that moment of doubt when someone from Microsoft questions you.
I was able to find this golden nugget of information, written by David Sanchez entitled Azure Application Gateway uses the Load Balancer. This confirms that it is a built in to the Application Gateway by default using an algorithm to provide load balance services.
So in short, yes the Application Gateway WAF, does include a Load Balancer, it is just inbuilt and therefore shielded from configuration choices.