Can OFP's standalone dedicated server run on Linux?

As of OFP version 1.85, yes. Here are some download mirror links for the latest version, the OFP version 1.90F beta Linux server file:

BIS

You can read the OFP Linux server installation instructions here.

For OFP versions prior to version 1.85, you can download home-brewed instructions and test out the unofficial method of running on Linux from here.