Dynamic routing over inter-VDOM links
BGP is supported over inter-VDOM links. Unless otherwise indicated, routing works as expected over inter-VDOM links.
If an inter-VDOM link has no assigned IP addresses to it, it may be difficult to use that interface in dynamic routing configurations. For example BGP requires an IP address to define any BGP router added to the network.
In OSPF, you can configure a router using a router ID and not its IP address. In fact, having no IP address avoids possible confusing between which value is the router ID and which is the IP address. However for that router to become adjacent with another OSPF router it will have to share the same subnet, which is technically impossible without an IP address. For this reason, while you can configure an OSPF router using an IP-less inter-VDOM link, it will likely be of limited value to you.
In RIP the metric used is hop count. If the inter-VDOM link can reach other nodes on the network, such as through a default route, then it may be possible to configure a RIP router on an inter-VDOM link. However, once again it may be of limited value due to limitations.
As stated earlier, BGP requires an IP address to define a router — an IP-less inter-VDOM link will not work with BGP.
In Multicast, you can configure an interface without using an IP address. However that interface will be unable to become an RP candidate. This limits the roles available to such an interface.