You could think of Sugar as a desktop environment like KDE or GNOME (architecturally, it is sort of a cousin to GNOME). There is more to it than that, but it'll do for starters.
It should be possible (in the future) to allow a student to chose whether to log into GNOME or Sugar on a LTSP terminal. It also should be possible to allow them to run Sugar as an application within their regular GNOME session, in full screen or windowed mode.
Sugar is extensible through its own packaging system.
And it is certainly not flat; if it fails, it will be because they're trying to go too deep.
Thanks for the explanation, I thought of Sugar more as an OS and not just a window manager. Very cool. Tom, maybe you could get Indiana on board and bring OLPC to the US :-)