Q. If I use Network Peering to connect Virtual Networks together can a connection from on-premises connect to peered networks?
A. When virtual networks are peered there is an Allow Gateway Transit option. If this is enabled then connections via ExpressRoute or site-to-site VPN to a virtual network will also be able to access virtual networks that are peered via network peering. This is shown below. In this example providing gateway transit is enabled then on-premises would be able to connect to Virtual Network 2 via Virtual Network 1.
More information on network peering can be found at https://azure.microsoft.com/en-us/documentation/articles/virtual-networks-create-vnetpeering-arm-portal/.
Note that if site-to-site VPN is used to connect virtual networks then the transit routing would NOT apply. In that scenario each network (including on-premises) would have to be connected in a full mesh topology. For ExpressRoute connect all virtual networks to the same circuit which will enable full connectivity.