My guess is the second person would be given at least 1 free checked bag due to your AmEx card (even though technically they need to be on the same reservation). I kind of doubt they would be given 2 free checked bags, since they are not on your reservation and also technically don't accrue your FO benefits.
I know that if everybody is on my itinerary then my luggage allowance is given to everybody. I.e. on a flight across the Atlantic with 4 people this summer we could take 8 pieces of luggage.
With the two itinerary I guess that the computerized check-in won't give the allowance on the other itinerary. What I wonder if the agent will allow it though since I was forced to purchase the tickets on separate itineraries.