That's not quite like my setup--I have a matrix switch between the WDTV and the splitter, with other inputs on the switch as well--but your drawing is correct for what you want to do. And you do want a splitter for that job, not a switch.
There's no guarantee that any given splitter will work with all your devices because of the aforementioned DRM stupidities but the only problem I've had with mine was when I was feeding one output to HDMI In on a projector and the other to DVI In (through an adapter) on a computer monitor. Sometimes it worked, sometimes I got a colorspace mismatch on one of the displays (shows as pink or green tint, like The Matrix only worse). My solution was to replace the monitor with one with HDMI In.