If you're asking if you can access your home copy of Access from a CGI running on your (non-home) web host, the answer is a qualified No, with the proviso that my knowledge of Access stop with Access 2000.

If Access 2002 is a true server (i.e., one you can connect to via socket), then you could arrange to have your home box periodically broadcast an IP address to your web host. Then use this IP address in your DBI connect string. Unless you could set up a selective firewall, this would mean exposing your (Microsoft) database product to the world at large. Recent history has shown this to be a Very Bad Idea.

An alternative is to delegate work back to your home server at a higher level. This also requires that your home server periodically publish its IP address to your web host, and requires that you construct a server process that listens for requests, translates the requests into SQL, then bundles up the results to transmit back to the web host CGI, which then needs to unpack and display them.

Another alternative is to see if your web host supports MySQL, then bite the bullet and upgrade your database.