That's what I thought you were using.
It cannot produce a valid date.
If the input was constant and the atmosphere was not in equilibrium then you could conclude that the age of the atmosphere was less than the time taken to reach equilibrium.
However if there were an event that significantly affected the amount of C14 then that would upset the equilibrium - and we know that such an event has happened in the last few decades. Nuclear weapons tests have produced extra C14.
Worse, if the input is not constant then there is no reason to expect the C14 to settle down to an equilibrium - or to stay there if it does. And if it did it would be disturbed as soon as the input level changed again. We know that this is the case, too. C14 is normally produced by cosmic rays - and therefore depend on the cosmic ray flux arrivng at Earth. And that is not constant.
So - whether the atmosphere is in equilibrium with regard to C14 has nothing to do with its age.