No, log files are stored just as everything else in the same direcory structure. You can move the complete structure including gcodes, projects etc if you want by adding a extra configuration file telling where to look for it, see
https://www.repetier-server.com/startup-configuration/<br/><br/>What you want is a extra xml with
<storage-directory>nowFolder/</storage-directory>
pointing to new disk and have a exact copy of the existing folder there when you start the server service again. I'd use the extra xml file in program folder so you can remove the old directory afterwards.
An other driver on same computer is ok, network drive is nothing I'd do. It is slower in access and a network failure will break prints.