AFAICT Emacs receives enough information to see S-SPC?

Hitting SPC and S-SPC 3 times each from emacs -Q (so without calling
(pgtk-use-im-context nil), and with dead keys fully functioning):

> space
> space
> space
> Shift_L
> S-space
> S-space
> S-space

No idea how easy it would be to pass on that information to the rest of
Emacs.