Hi lilucemj,
You ask an interesting question; the answer is completely dependent on how much the half-Marathon will 'wear you out.'
In general, I'm a bit concerned about the idea. Even at a casual pace, you'll be running for 2-3 hours and THAT will require a serious effort and a certain amount of recovery time. However, you seem to be 'juggling' all sorts of things in your life right now, so you might be able to handle all of this just fine.
During your training for this race, have you ever taken a FULL-LENGTH CAT the day after a long run? If so, then how did you score? If not, then were you able to study effectively the day after a big run? Were you able to stay focused or were you just too tired overall to stay sharp?
How soon is all of this happening? When is the race and when is your GMAT?
If you have some time, then you might want to 'test' this all out. Do a normal training day, then try to take a FULL CAT the next day and see what happens.
GMAT assassins aren't born, they're made,
Rich