I don't think that backwards compatibility for SQL 2000 is still supported. So it might be that your code behaves "differently" in some subtle way with a newer version. Chances are good that it will be fine, but you might want to test just in case.

You will also have issues restoring a SQL 2000 database to the latest version of SQL. Latest version that you can restore SQL 2000 backup to is, I think, SQL 2008. So you would need a SQL 2008 version of SQL to make the restore. I would suggest that you do that, backup again, and then restore to the latest version of SQL (2014 or perhaps 2016 by the time you do this), otherwise in 4 years time the problem is going to be even more difficult 🙁