Yes, there is debate over whether or not GABA crosses the BBB - but it appears that large doses (whatever dose that is) can cause GABA to cross the BBB. It also seems to me that, from personal experience, it works for improving sleep. From researching online, it appears that many others agree that they see improved sleep with it.
So, I guess, a few things could be going on.
1. We could be wrong - it does somehow cross the BBB.
2. Maybe taking it exogenously is "sparing" in that it can still be used throughout the body, which means you can use more of your endogenous GABA in your brain.
3. Maybe just the fact that it relaxes your body, even though it isn't acting directly on your brain, sends the signal to your brain that you are relaxing/sleeping. Your body does interact with your brain of course, and if GABA can shut down nerve impulses in your body, your brain should follow.
4. Maybe a combination of the above, all of the above or none of the above.