So you got both extremes of answers here .. let's elaborate some.
On Windows, the concept of a "UNC path" is pretty clear and obvious. There's system software like the Multiple UNC Provider and Network Redirectors that help the Windows OS map open requests for UNC paths to remote hosts and so on. From that perspective, @esix_splunk's answer is mostly right. I might have used [monitor://\\\\servername\sharename] instead given the syntax is monitor://. One thing about this approach is that your user running Splunk must - from a Windows perspective - have the appropriate access to be able to reach the CIFS share. This can be ... problematic ... if you are running Splunk under its default "Local System" user. You would have to enable Splunk to run as a Domain Account in order be able to reach CIFS shares. This is a Windows limitation, not a Splunk one.
But, you explicitly said "Linux". In fact, you said "Both the Splunk server and the log files reside on Linux boxes". If that is the case, why in the world are you asking about CIFS? For Linux to Linux, NFS would be vastly less painful to set up. But, if you must do CIFS on linux, observe there's nothing like UNC paths there. You need to actually mount the CIFS filesystems somewhere onto the filesystem tree. Several examples of ways of doing this are in the CentOS Documentation.
All of the above will work, but as @muebel said, best practice is to use a forwarder. Install the Universal Forwarder on the box with the logs, and let it forward to your indexer. This is best practice because mounting a remote filesystem (be it NFS, or CIFS, or Linux, or Windows) introduces a tight coupling between the two hosts. A forwarder is much more robust when problems do come up.
