Can FME read a file on a UNIX server file directory?

I would say that it depends on a lot of factors that have little to do with FME. But if you can access the unix server directory from the server where FME is running (Windows, Mac or Linux), then it should work.

Thanks for that. Yes the unix server is the same location that FME is running on (Windows Server 2008). Is there parameters in FME that I need to configure?

I assume that you'll access the Unix share over a UNC path. The Unix share is something that your Unix admin needs to configure and to give you the corresponding UNC path. On FME you simply need to configure the service account and make sure it has permissions to access the Unix share. See also http://docs.safe.com/fme/html/FME_Server_Documentation/AdminGuide/Running_FME_Server_Engines_Under_Different_Account.htm