Yes, it will reabsorb as the pressure rises thru the free surface. That's Henry's law.
Again, the brake system is (largely) sealed. Car systems I've seen have a very small breather in the master cylinder. I would imagine bikes do too but I did ask what the rate is especially down at the calipers, but the fluid isn't just sitting there out in the open.
So sure, air will be reabsorbed but it won't happen instantly. It's quite possible for road use this isn't worthwhile over the longer term. For racing, it might be a different matter.