Probably doable, but not without a lot of trouble. It's a 1200, you say? Just get yourself a PCMCIA network card, easy-peasy! 
That's what I did for my non-towerised A1200. Some years back, work was throwing out some old PCMCIA network cards so I grabbed one to try out and it worked great. Just configured it for the LAN and let the ADSL router worry about the internet connection.
