It happens all of the time. For many situations, there is considerable risk in letting somebody hang around for two weeks. The employee's mind is going to be elsewhere. He will be excited about the new job, and eager to talk to co-workers about the move. The employee may even decide to save some of his more valuable work to use in the next gig.

The manager is almost always better off by letting the departing employee off immediately to hedge risk. You pay him for the two weeks, and let him sit at home.

What I find most puzzling is why announce the resignation via email? This is almost always best done face to face, or at least via phone. Doing this electronically strikes me as immature.