>> Presumably this can be done?
Yes, you can Backup & Restore the 2000 databases in 2005 server.
Alternatively, You can also perform Detach and Attach databases.
Kindly let me know if you need any help on that.
>> And that apart from the production database, the system databases (msdn and master) will also have to be copied over?
Not recommended to move 2000 system databases to 2005 system databases.
Instead perform the following:
1. Create all jobs present in 2000 server to 2005 server
2. Create Integration packages if any as SSIS packages
3. Create Maintenance plans and Agent jobs if any present in 2000 server
4. Transfer logins from 2000 server using the script provided here
http://support.microsoft.com/kb/246133