After all, 31 has almost certainly had Andorians in their ranks since United Earth became part of the Federation. And probably still had
Andorians in their ranks even after the secession vote.
In any case, I can't see "the bureau" not wanting a positive outcome re: Andor rejoining the UFP by way of Bashir's actions or those of anyone else they knew of with an interest in making it happen. They may be pragmatists, and they're certainly ruthless. But loyalty to something does imply a sentimental streak in there somewhere.