Yes, I also often use the Power "button" of the LCD monitor, as I did for the CRT (can't really remember). The screen saver app works here with VGA, HDMI, DVI connectors. Haven't tried with a DVI - DP converter, due to lack of an adapter. The on-board jacks are VGA, HDMI and DVI, the monitor has them all: VGA, Composite, HDMI, DVI, DP.
All these on-board connectors work with the screen saver (only tried blank screen). Haven't tested another machine with DP, but may follow in far future.
I had the LCD for a long time connected via VGA (was another machine with a Matrox), but then have also tried other interfaces. It took a while, but now I think the blurry display of an analog connection looks worse. Of course, monitor settings have to be adapted. I have both Brightness and esp. Contrast set to lower values.