Earlier quoted context omitted.
Unfortunately, trying to defeat side-channel attacks by adding random noise usually only increases the number of samples required to extract information, rather than preventing the attack entirely. (You can blame the central limit theorem for this.)
This is not entirely true. Or rather: it is true when the countermeasure is to add random delays to pad out overall timing, since one can simply collect more samples to obtain an average. And that may be what the OP is suggesting: just scale the frequency to random levels that are not quite the pre-programmed ones, which is very similar to adding random delays. (In practice this might actually work well enough to def…
Eg. my app is performing digital signatures and I'm sure that they take <1ms CPU time, but performing digital signatures in 10ms is acceptable for my application, so when I perform a signature I measure the CPU time elapsed, say 0.5ms and then wait for 9.5ms.