A couple more:
Dia: Allows leading/trailing spaces, they can be selected (there is no visual hint), they're included in the highlight/selected effect (no bbox to speak of).
SVG-edit: Allows leading/trailing spaces, they can be selected, they expand the "object area" (it's some kind of bbox, but doesn't appear as tightly defined as ours is).
I tested LibreOffice Draw (4.2.3rc3) as well and see no cursor change under any circumstances. The leading/trailing is not selectable, but if you click close enough to the object boundary it will select the object (so the area above, below, and to the side of the first/last space). A text object containing only spaces can be select by the same way, but with no visual hint, so you have to know where to click.
Cheers,
Josh