Short answer: No.
The campaign overview gives guidance on how to use devils in Rise of Tiamat. What follows may contain spoilers for the Rise of Tiamat adventure.
It is stated in the section Hosts of the Nine Hells that Tiamat is something of a prisoner of Zariel, and Zariel wants to be rid of her. For this reason, Zariel has instructed her mortal agents to assist the cult in summoning Tiamat away from Avernus. On the other hand, this ideal is not universally supported in Avernus. It is stated:
However, just as Zariel wants Tiamat out, other devils would be happy to see the Dragon Queen stay in Avernus. Foremost among them is the deposed pit fiend Bel and the devils still loyal to him.
This section goes on to suggest even using devils to assist the party in their quest, albeit for a devilish price. So it would be perfectly within the modules guidelines to have this bearded devil be loyal to the pit fiend Bel - Tiamat be damned!
To directly answer your question, it would seem Tiamat has no authority. Prior to being erected as ruler of Avernus, Zariel was in some way subject to Tiamat, something that "rankles her still". Zariel cannot kill Tiamat, but Zariel is in charge now. If the particular devil is faithful to Zariel, then that devil may obey Tiamat since both Zariel and Tiamat want Tiamat gone from Avernus. But if the bearded devil is faithful to Bel, the devil is going to tell Tiamat to pound sand. Bel wants to keep Tiamat in Avernus.