Can I install the Exchange Server 2003 version of Exchange System Manager (ESM) on an Exchange 2000 Server system?

Well, you probably could find a way to trick the Exchange 2003 installer into putting ESM on Exchange 2000, and you might even find a way to force the new ESM to coexist with the existing Exchange 2000 version. But neither Microsoft nor I recommend the combination. Frankly, you're likely to break something in the process of trying to jam these two parts together. But let me suggest an alternative: Install the Exchange 2003 ESM on your administrative workstation or another non-Exchange server, then use Terminal Services (or Remote Desktop if the workstation runs Windows XP) to access ESM 2003.