Can an exchange server (2003) handle an ip address change? Without breaking the exchange install?
The answer is, "Yes, this is possible." The reality is that if you didn't set up that mail server, and/or if anyone else has been in a position to change its configuration, it's likely that there are settings buried in that server which will cause glitches in this process.
E.g. I managed an Exchange 2003 server with DNS hard-set in Exchange, even though the server (at the time) was using the same DNS settings via NIC config. Took a while to ferret out the redundant setting throwing a monkey wrench into our network DNS change effort.
The moral of my ramble is that Exchange has a WIDE variety of opportunities to make a simple task explode into an overnight fiasco. I would test your change in a virtual or sandbox setting ahead of time if it's even remotely possible.