No, PDF Explorer manage itself the database files, there are not an independent database server to where more than one PDF Explorer instance can connect.
You can however:
Put all the PDFs in the server PC, acting as a data server, and run PDFE, with web server enabled, from your desktop. You can index and edit all the PDFs, and all the LAN clients can access your desktop PC running PDFE Web Server.
or
Run PDF Explorer in the server PC, and access to it with remote desktop from your Desktop PC, to make the necessaries updates.