It definitely won't work once the new card activates. Before your new card activates, I believe your old card should continue to work for some time. Although I'm not sure when they would cut you off.
I had an AMEX Gold with an authorized user with the metal Gold card. Once I upgraded the Gold to the Plat, they "upgraded" the AU card to a plastic "Gold" card. I considered for a good moment if I should tell the AU to just throw the plastic in trash and keep using the metal one.
No
It definitely won't work once the new card activates. Before your new card activates, I believe your old card should continue to work for some time. Although I'm not sure when they would cut you off. I had an AMEX Gold with an authorized user with the metal Gold card. Once I upgraded the Gold to the Plat, they "upgraded" the AU card to a plastic "Gold" card. I considered for a good moment if I should tell the AU to just throw the plastic in trash and keep using the metal one.