Double-pole, 240-Volt, 15 Amp GFCI circuit breaker to create two 15amp 120 circuits for switched split receptacles
Yes, that's totally fine.  What you are proposing is called a multi-wire branch circuit in 120/240 split-phase.  They are falling out of favor because protecting them with GFCI or AFCI is a challenge. You must either 


fork the circuit and place AFCI/GFCI after the split; or 
use an expensive 2-pole GFCI device.  This is the option you are proposing. And that is fine. 


A 2-pole GFCI is built the same as a 1-pole GFCI, it just has 3 wires going around its magnetic sensing core instead of two.  All current heading out on L1 must return via either L2 or N.  Current flowing out on N must return via L2.  Since all 3 wires are wrapped around the magnetic core, each combination causes equal and opposite magnetic flux, which cancel each other out.  

After working with 1-pole GFCIs for awhile, ones armchair kneejerk may be to say "that can't work".  Take the time to diagram it out and think it through.  It works fine.