I tried this and it worked for some of my users and not others. I discovered the problem to be that 2000 supports 7.0 encryption but some of my users were created when we were running 6.5, and that encryption is not supported.
One other thing I did when I upgraded from 7.0 to 2000 is I scripted out the users SID, so when I migrated the SID's matched in the corresponding DB's. I also did all of this on the production server than transfered all of the users and sid's to our test environment, this was so when I restored a db onto test I would not have to remap any logins. One last thing is when you move to 2000 make sure you create the db's so that they have the same dbid. This fouled me up with the users default db setting.
Hope this helps.