@bsieker
I think, the chances of your scenario leading to a mid-air collision will be rather low. As my knowledge on TCAS algorithms is mostly based on the Ueberlingen accident report, it is an educated guess, though.
This is how I think the system will work:
aircraft 1 (TCAS) get's RA descend.
aircraft 2 (ATC) get's instruction descend.
Both aircraft will descend following SOPs (1.25g, reaching approximately 1500ft/min descend rate).
TCAS onboard aircraft1 will monitor conflict situation. If aircraft 2 is lower than aircraft 1, TCAS will issue a Level off or perhaps a Reversal RA, if aircraft 1 is lower than aircraft 2, it will issue an Increase RA. In case the altitude of aircraft 1 and aircraft 2 are identical, I think TCAS would vote for an increase RA, as this would probably be more comfortable for the passengers and the course of action would be more straight forward (but this is only a guess).
In the Level off/Reversal RA scenario, aircraft 2 will continue its descend with 1500ft/min, aircraft 1 will reduce its descend rate. As aircraft 1 was above aircraft 2, the chances are, that both aircraft will avoid a mid-air.
In the Increase RA scenario, aircraft 1 will increase its decend rate following SOPs (1.25g, reaching approximately 2500ft/min). As aircraft 2 will continue its descend with 1500ft/min and aircraft 1 was lower than aircraft 2, chances are, that both aircraft will miss each other.
Both scenarios are based on the assumption, that ATC does not give further instructions to aircraft 2 after the first "descend" order.
If ATC was monitoring the situation, the controller could have noticed, that aircraft 1 was descending. In this case, the heshe could have issued a "level off" order to aircraft 2.
This case only has an impact on the "Level off/Reversal" Scenario above, where it would reduce the chances of both aircraft avoiding a mid-air.
But the premises for this last scenario would be rather high, as conflict recognition systems at ATC most probably will identify the conflict situation between aircraft 1 and 2, influencing the controller's actions.