Au contraire; according to the Battle Subway OP,
While taking the Subway challenge, all Pokemon you bring with you cannot be being used in any other roleplays in ASB, nor can they be used in other battles in ASB while the Subway challenge is ongoing. By bringing a Pokemon with you for the Subway Challenge, you effectively remove it from the rest of ASB until your challenge is over.
I also discussed the DQ with Flora, and she's behind it.