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 defeat delicate attacks.) However what I hoped the OP was suggesting is to add random instructions as a way to prevent the processor from switching power modes: sort of like tapping your phone screen occasionally to keep it from dimming.

There are also other (unrelated) techniques that use randomness to eliminate side channels. One of the most basic anti-timing-attack countermeasures is to use RSA blinding in which a base C is first randomized by computing C^r mod N before that (random) result is combined with the secret key. The randomness can then be removed from the final result. This defeats attacks that depend on choosing or knowing the value C.