you can. it's not tested. i believe the 11g drivers support communicating w/ a 12c db... is there a reason you need to change it out ?
Our DBA is recommending it as a best practice as well as the Oracle Support site mentions possible issues using lower version drivers with higher version databases.
Can you provide the steps on how to upgrade the Drivers? I did a quick look for the Jar file but couldn't find it.
There should be a oracle—jdbc-11.2.jar in the NSH/br/stdlib dir. you can rename the 12c to the same name and replace it, or find all instances where the 11.2 jar is referenced in various startup scripts and change it.