Are we forgetting that climbing or descending is not the only way to avoid colliding with another aircraft? If you're descending because of a depressurization, you're not necessarily on one engine, and you always retain the option to maneuvre laterally.
Simply arresting the ROD briefly might be enough to escape the danger. You don't HAVE to CLIMB.
As for calling 'mayday'...didn't you squawk 7700? Your hands and minds are full of other business in an emergencty descent, assuming it's not your own window that has let go...