VPN servers wouldn't hand out BGP routing updates. That would all happen on the routers which would be BGP neighbors.

What the best way to do it would be to but your VPN server in a DMZ and set your client sofware to connect to that IP address. If you were doing a router-to-router or firewall-to-firewall or even a router-to-firewall VPN, then both sides would have their crypto peers defined so it will know where to go. It would know where to go once it hits the router and the router looks up in it routing table where to send the packet. BGP or any routing protocol is transparent to the actual VPN connection itself.