Is there a way to turn off an external Apple Cinema Display remotely and continue to use the computer?

I don't think this is possible with Screen Sharing. (That would go against the "spirit" of the Screen Sharing feature, which is to help people troubleshoot a problem or work collaboratively on something.)

This is not a free alternative, but if you use Apple Remote Desktop ($80), you have the option to "curtain" the screen, which not only hides what you're doing, but locks the remote computer against local access. It also has many powerful system maintenance/monitoring features.

As far as saving power, could you simply turn off the local display before you leave the location? You should also set the display to sleep when it's not being used (in the Energy Saver pref pane) -- in that case, it would only be drawing power while you're connected and using it. Also, if you're using one of the new LED Cinema Displays, keep in mind they are energy efficient devices, so the power draw isn't as much of a concern as with standard (non-LED) displays.

If your computer is running or is capable of running OS X Lion, or OS X Mountain Lion Screen Sharing is able to use a feature called Virtual Display to allow remote user a view that does not mirror the actual screen on the Mac, not sure if energy saver is able to know about the Virtual Display and not keep the Physical display active, but it is worth a try.

As noted in What's new in Lion: AirDrop and screen sharing

Screen Sharing under Lion has been significantly enhanced. To begin with, it’s now possible for you to not only view the display of another Mac, but also share the screen for any account you have access to on that Mac, even when someone else is using it with another account.

For example, let’s say a remote Mac has two user accounts—Joe and Jane. Joe is currently working on that Mac in his account. From another Mac, Jane can select that Mac under the Shared heading in a Finder window, click Share Screen, and enter her user name and password in the resulting dialog box. When she clicks the Connect button, a Select Display window appears. Within this window are two options—Ask to Share the Display and Connect to a Virtual Display. If she clicks Ask to Share the Display a message appears on the other Mac indicating that Jane would like to share the screen. If Joe clicks Share Screen, Jane can see what’s on Joe’s screen as well as control Joe’s account.

Additionally according to OS X Mountain Lion: Share the screen of another computer the feature is also available in the brand new Mountain Lion OS too.