Yes, you can have both on the same computer. Many of us do.
There are a few gotchas:
1. Make sure you do a custom install with multiple versions, so you can
check they go into different folders and don't uninstall each other. (Should
be fine for your case, but worth checking.)
2. You may have versioning problems with things like the Calendar control or
MS Graph.
3. There is a problem where Access 97 refuses to start, complaining "There
is no license..." If you strike that problem, see:
http://support.microsoft.com/default.aspx?scid=kb;en-us;141373
4. If you double-click an mdb in the Windows Explorer, it will probably try
to start in whichever version you ran last, since both versions check and
register themselves when they start.
5. If you convert an A2003 version back to A97, it will sort out the Access
and VBA references correctly, but it may leave the DAO library at 3.6.
That's wrong for A97, and can give you problems if you don't manually set it
back to 3.51.