Yup, works fine...
Right now I've got Parallels full screen on my primary display, and this Safari window on my secondary. (After digging up a second display and my adapter...)
And now I've got Parallels full screen on my secondary display, and this Safari window on my primary. (Which really makes more sense, since you don't want the Mac menu bar appearing over the top of the Parallels display, now do you?)
Unfortunately, taking a screen shot with Cmd-Shift-3 produces two files, one for each screen. Let me try Grab real quick. Ah, yes, using Grab and capturing 'selection' works. Just drag it across both screens. (Had to make them the same (non-native on the primary) resolution.)
I like how the shadow from the Safari window carries over onto the Parallels screen... I didn't notice that until I looked at the screenshot.