I'm working on a project with a customer who already has VNETs in West Europe, Asia East and North Central US, two which have ExpressRoute connections and the third with a S2S VPN (obviously with relevant FWs and GWs). The plan for the AVD deployment is to use the West Europe VNET as the core services hub and peered spoke VNETs just for the workload AVD desktop pools in the three regions. My question is, can I/should I also peer the new AVD regional VNETs to the corresponding pre-existing local VNETs (e.g. Asia East to Asia East) and configure routing tables in each to direct traffic out locally, rather back though the core in West Europe, or if that will even work?
Short answer - yes, you can peer your regional networks and configure default internet route to go out locally
To make AVD work you need to have a traffic going out to the Internet (with a default route or using the Service Tag), it is recommended to route Internet traffic directly out of vnet, without sending it on-prem or sending it to another region. Additionally you need to take care of AD connectivity within a vnets, so you would probably need a peering for your private subnets.