after you beat the elite four the moment you come down from your room or leave your house something happens. it could be the start of the delta episode or the handing of a starter from the professor, but no one of these events cancels out any of the others.
note: when birch does have a Pokemon for you you are forced to walk to him as soon as you leave the house, if you walk to rt.101 of your own free will nothing happens.
source, experiences