I wonder what happens if you have an arena game in progress on the site, from your browser perhaps, and then go to try to start a DGT game in the app? Will it see you have a game in progress and switch to it?
No, as far as I know the chess.com app connects to the Pegasus board only when playing free games using the two green buttons "Play" and, after enabling the slider for the board, "Start Game", not for tournaments or computer bots. Correct me if I'm wrong.