No. The link you gives mentions that the decay rates of radioactive particles are changing, this saying the half life is changing. Atomic clocks are based on the frequency of light emitted from an electronic transition. Ie, an electron makes a transition from one state to another and emits a photon, then we compare the frequency of that photon to another photon which has a nearby frequency, we measure the difference to like 8 digits, then use the frequency of the light produced from the transition as the inverrse unit of time.

One is based on nuclear decay, the other an induced electronic transition and not affected by unknown variations in the half life.