I have this friend of mine who's in Tuck. He also applied to other top programs and told me that you self report everything. They'll run a check for your scores only if you get a spot in the class. I don't think you should worry about the "arrival" of your scores to Bschool... There's plenty of worrying to be done for the exam itself!

They don't take very long at all.

Once you write you will immediately receive your Quant, Verbal, and total scores unofficially at the test centre. As DanaJ mentions, some schools will allow you to self report these results immediately. Obviously if you lie they will find out.

I wrote on April 9th, the essays were marked the next day and a Official Report created. On the 11th I got an e-mail with a link to the official report. On April 14th I got an e-mail saying the Score Report had been sent to the school my choice. Later on I got the Official Report via snail mail, but everything had been settled by then.

Officially the GMAC gives themselves a 20 day window, but in my experience it was much faster. If you are coming close to the deadline, speak to the school representatives about self reporting.