From my experience they will cancel neither. They could/would cancel if you had 2 bookings on the same flight or on the same route. You may want the flexibility and if you book 2 tickets all the better for them.
However you expose yourself to repricing or Avios reprisals on the ex-EU flight to the US if you never had any intention to take the last leg, and that is emphasised by the simultaneous booking to BHD. The risk is very limited, and perhaps one way of reducing it is to not have your Exec Club details in the BHD booking nor your real date of birth.