<<I just want to confirm, if we run a task to remove the three files on our deployed desktops, can we still remote control a client/PC via CMS?>>
I sent the job to a test machine and confirmed this to be true, but I would suggest you testing before sending it as well.
<<Also, where do we uncheck the user approval box>>
In CMS, settings, Agents and Plugins, all agents, remote mgmt, remote control, windows, pcanywhere settings, "Require user to approve connection" and there is also a timeout value there. There's also an authentication tab there that you should set if you haven't already probably, such as AD group containing Helpdesk Techs.