Can we use the Exchange Server 2003 version of Exchange System Manager (ESM) to manage our Exchange 2000 Server systems?

For the most part, yes—although Microsoft doesn't officially support this configuration. Many administrators would like to use the Exchange 2003 version of ESM to manage Exchange 2000 servers so that they can take advantage of the improved (multi-threaded) mailbox mover and other nifty features. The drawback to this approach is that this version of ESM doesn't let you manage components that don't exist in Exchange 2003. For example, you can't use the Exchange 2003 version of ESM to manage the Exchange Instant Messaging (IM) service, the Exchange Key Management Service (KMS), or the various Microsoft Exchange Development Kit (EDK)−based connectors. Other components also might not work properly.