Can OS X be remotely accessed using the GUI but securely to hide what is displayed locally?
Yes - there are several ways around this. 

The free, but less elegant solution is to make a second account on the Mac you wish to keep private. Set the machine to boot to that user and use Fast User switching to switch to your account. 

Then when you log in - it will ask if you want to share the dummy account's screen or make a second virtual (and not drawn on the monitor) screen.

Alternatively, buy Apple Remote Desktop and use the "curtain mode" where it obscures the screen to hide what the remote operator is doing.