(Underline mine)

No, you only get the BIS miles you will fly. You also get to pocket the points earned from the tickets your charge to your Amex card.

As trooper pointed out, you don't get all the miles for the other 7 tickets unless you transfer them into your personal FF account. However, the transfer fees one has to pay to the airlines literally make it cost-prohibitive.

One exception is flying airlines that allow "household accounts" if all the 8 passengers from your trip fits the airlines' criteria for "household." Unfortunately UA isn't one of the airlines that offer household accounts.

Here's an old thread on the household accounts which may be dated since some airlines have tightened up the terms for sharing miles/points, but at least you'll learn what and where to start your research:

Who has "family" accounts?