It's not clear from your question whether you're going to be installing
Office 2003 Standard (which doesn't include Access) or Office 2003
Professional (which does).
The default file format of Access 2003 is the Access 2000 format, so you
shouldn't have any incompatibilities in that regard.
However, any time you install new software, you run the risk of corrupting
the References collection in your database. This is because Access is very
sensitive to versions: you (generally) need the same version of each
referenced file to exist in the same location on all machines. Fortunately,
the fix is very easy. Check
http://www.accessmvp.com/djsteele/AccessReferenceErrors.html for details.