The essays will not be graded by anyone from MGMAT, no. Only the multiple choice portion will be graded.
FYI on two things:
1) The official test writers offer a service called GMAT Write (
http://www.mba.com/mba/store/ProductInfo?SKU=1623X). The essays you submit will be graded by the same software used to grade essays on the official test, and you also receive feedback on how to improve your essays.
2) It is cheaper to buy one MGMAT book (which gives you access to the 6 tests) than to buy the 6 tests alone. The only drawback is that you have to wait for the book to arrive in order to log in and start using the tests - though, if you live near a bookstore that sells our books, you can buy the book physically at a store and start to use the tests right away.