I am not sure if dropping the first leg is permitted on American stock.
Their policy is different and much limited compared to British Airways when it comes to rebooking flexibility.
By the way, for the question of
Flyer1508 , some people who have booked tight connections in MAD now have an infeasible connection because of the MCT at Madrid as the CMN-MAD flight is departing a few minutes later than it was originally going to depart. For reference, the people I know that booked the tight connection has booked it to have the A350 from Madrid to Heathrow as all the remaining flights the same day were operated by a narrow-body.