Not at this level. The Rb resonance in question is ~6.8 GHz, which means that counting it (which is functionally all atomic clock is really doing) will give you accuracy higher by definition than the cycle time of the CPU running your timing-sensitive application.
GPS needs that because at the speed of light in vacuum that corresponds to ~2cm of wavelength, which is only 2 orders of magnitude from the design accuracy of the whole system.
Cycle-to-cycle accuracy of an atomic clock (then called a timing and frequency standard) is never dominated by the resonance frequency, and you never extract the timing information from the radio-frequency that interacts with the physics directly.
The reference frequency used externally for timing is the reference oscillator which typically was 5 or 10 MHz, but nowadays tends to be 100 MHz as HF electronics became better.
{a Rb clock is very similar electronically, only you are not looking at count-rates of Cs atoms flying through your spin filter but you are observing the optical attenuation of a rubidium gas, both vary with radio-frequency waves being injected into the package. Also Cs is a primary standard and Rb is very stable - but adjustable and susceptible to extarnal magnetic fields.}
From the reference frequency, a series of synthesizers / multipliers generate the radio frequency that is relevant to the physics process. And this frequency is then modulated slightly (137 Hz label in Figure 5) so that correlation in the physics process from being too high, or too low in resonance frequency, can be observed (Figure 9, you vary between f2 and f1 137 times per second).
A good GPS steered quartz oscillator will use around 100s of loop time-constant, the time constant for the control loop in a caesium clock will be much higher.
I'm not following your ire. I don't understand why you think adding all the detail above is inconsistent with "functionally, all an atomic clock is really doing is counting cycles (and, OK, tracking phase) of a known transition of some isotope or another. You're just describing how.
GPS needs that because at the speed of light in vacuum that corresponds to ~2cm of wavelength, which is only 2 orders of magnitude from the design accuracy of the whole system.