short: no
long: unless you have changed your keyboard mapping, shift+space will send just space.
Aside from a few other special keys (Enter), you might expect shift to modify the character(s) sent by the keyboard. This is not always the case. Most of the ones you are familiar with are based on xterm, e.g., using shift, control and alt (or meta) to generate different escape sequences.
tmux "knows" about the xterm keys (and has a mode which can be set to permit it to use those keys). Otherwise (if xterm-keys is not set), if the key matches the terminal description for one of the known special keys (function- and cursor- and editing-keys such as Home and End), tmux accepts that key (and maps it into the screen or whatever "internal" terminal description is used).
If the key does not fall into one of those categories, tmux ignores it (discards it).
So... if you want to use shiftspace, you will have to make it send one of the escape sequences which tmux expects, and make your binding against the corresponding predefined capability.
Further reading:
