The short answer: Absolutely NOT!
The details: Your machines need to be able to alk to each other over the network using TCP/IP. If you have not setup TCP/IP on your machines (which would be weird because you wouldn't be able to get to the Internet over your network) then you need to do so. It doesn't matter if you tell each computer what IP address to use or let DHCP do it for you. If you use DHCP, then make sure that you can resolve hostnames, like this:
[command prompt] % host mycomputer
...and that should return the IP address set by DHCP. If that doesn't work then I would recommend getting a conversation going with someone like myself, who can talk you through some of the things that you could do to fix it up. The main thing to do here is make sure that your DHCP server and DNS server programs will talk to each other. This allows DHCP assignments to be recorded and available via DNS requests.
Once you have your hosts resolving properly, you can do this on the REMOTE host (this is for a tcsh shell):
[command prompt] % setenv DISPLAY mycomputer:0
By using the computer's name, your connection will still work even if DHCP changes the machines IP address (assuming that your DHCP server is working correctly to report such configuration chages to your DNS server). This is especially nice in that you do not have to think about the IP addresses at all (once it is all up and running), just machine names (which are easier to remember and work with).
Lamont R. Peterson <lrp AT xmission.com AND_NOTHING_ELSE.net>