Connecting a Pseudo-Neutral to Pig Tail of GFCI
In that case you would hook the red "outside" wires to a 240V supply, i.e. A different 240V breaker.  That would cause the center black wire to synthesize a midpoint at ~120V.  

Since the GFCI breaker is getting its outside wires from the exact same bus bars, the center black would appear as a neutral to it, and should suffice to power it.  

GFCI devices don't care about safety earthing, so you're all set. 

It wouldn't work to attach the two red wires to the outputs of the GFCI breaker; those are inside the GFCI protected zone, and you intend to use the black (pseudo neutral) wire outside that zone, so it would be a fault, exactly what the GFCI is designed to detect and trip on!    

There is one problem, though.  There is no listed method for attaching supply power to that breaker; it's designed to snap into a Siemens service panel and engage its bus bars.  Therefore your best bet is to get a small Siemens panel that is  compatible.   That panel could support several such breakers: you could set it up as a subpanel.