You CAN definitely run sqlplus using a mounted drive. I am currently remotely logged into a windows 2008 server with NO Oracle software installed. I mounted a drive where Oracle is installed as X. From a command window I set ORACLE_HOME and added %ORACLE_HOME%bin to the PATH variable. I was then able to execute SQL*Plus from that command window. On a UNIX server this is done frequently. After reading the comments I couldn't understand why it would not be similarly possible on a Windows system.... so I tried it. By using a mounted drive it is like having the software locally. Just be sure all the environment variables are set appropriately and use the right connect string.
I beleive that you will need to have SQLPlus installed locally as you’ll need the Oracle drivers and tnsnames.ora locally.