There are two general scenarios which connect on-premises to Azure, ExpressRoute or Site-to-Site VPN.  If site-to-site VPN is setup from on-premises to facilitate communication between the AVS private cloud and the on-premises environment(s) Azure Route Server will need to be setup in the same Virtual Network where the AVS private cloud connects, and the Site-to-Site VPN connects.  Once Route Server is setup and configured both the on-premises sites and AVS will be able to communicate with each other.