Yes, you can. The Derby database is identical, regardless of whether it was accessible by a stand-alone program using the built-in driver or by several client programs associated with the Derby network server.
The Derby network server is simply “bonding software” that implements remote DRDA database protocols to implement JDBC-over-the-net, and then uses regular built-in database access to access your server-side database.
If you want, there is even a slightly more complex configuration called the “built-in server” that allows you to use your program, which uses the built-in driver, to access your database resource, which is accessed by other network clients, while acting as a network server.
Here is more information about this last option: http://db.apache.org/derby/docs/10.10/adminguide/radminembeddedserverex.html