Answer
It would be possible, but it would have several issues. Because gravity depends on altitude and longitude, there would be slight differences in the period of the pendulum in different locations. The modern method of using an electron in cesium to obtain a microwave with a frequency of exactly 9,192,631,770 does not have this issue, and of course is much more accurate, but one could make the argument that the pendulum would be a much cheaper and more approachable to the average man.
Work Step by Step
The period of a pendulum is given by:
$T=\frac{1}{2\pi}\sqrt \frac{1}{mgl}$
For a change of altitude, g would change by:
$g_{altitude}=g[1−R2h] $
where R is the radius of the earth and h is the altitude. Factoring this into the period, we get:
$T=\frac{1}{2\pi}\sqrt \frac{1}{mg[1−R2h]l}$
And we see that the period is inversely proportional to the altitude.
