I'm looking to set up a VPN (OpenVPN is my first choice but I'm not stuck with it) in such a way that the server that hosts the VPN is not visible from within the VPN. That is; any packet that a client sends via the VPN interface will get delivered to another client's VPN interface or get dropped. In the other direction, the server shouldn't have a VPN interface at all and normal network operations shouldn't be able to send packets on the network.

Can this be done?

All the docs I have found have assumed that clients will connect via DHCP (this requiring that the server connect at least to that extent) but I can't think of any reason that a VPN couldn't use static IP's or that the DHCP server couldn't be implemented inside the VPN (see edit) server without setting up a VPN interface on the server.

Edit: Based on the link on bridged mode from Phil Hollenback's answer it seems that OpenVPN does in fact have the "internal DHCP server" that I'm thinking of.