I investigated this, and unfortunately, the answer is no dice, for two reasons:
1) If you just plop a .mdb file onto a Linux box, there is no database server. In Windows, the server is the Microsoft Data Engine (MSDE - or the Jet engine for older versions of Access), which is really a set of system libraries for reading and writing to the access files. The Access ODBC driver lets you use standard ODBC database functions to manipulate these databases.
2) The Access file format is undocumented, so no non-Microsoft applications (AFAIK) can read and write to it directly.
If you plan to deploy the database on a Linux box, I think the simplest thing to do would be to move the data into a MySQL or Postgres database, and run your PHP against that. If you still need the Access front end to connect to the database, you can do so quite nicely with the ODBC drivers for MySQL and Postgres respectively. I've actually used Access with MySQL this way, and it works quite well.