Cybernetics was promoted as an alternative to market price discovery. Central planning removes or disrupts decentralized price signaling. This results in misallocations of resources in planned economies. The Soviets also briefly experimented with Cybernetics, but were unable to make it work. It was an attempt paper over fundamental failures of Marxist economics with technology.
DOGE, has thus far, focused on cutting spending. Elon has spoken about his hope to increase productivity in the private sector by cutting the public sector. Understand that from a market perspective, public sector spending is regarded as a misallocation from the productive private sector, because no price signals can confirm the value of spending.
While some will dispute that it is possible for the public sector to optimally allocate resources, without price signals, we are unable to confirm this. Typically from this point, advocates of public spending will appeal to a subjective "greater public good" which conveniently, is only known to the allegedly altruistic proponents of public spending. This isn't to say that market pricing always creates perfect outcomes, but that the moral hazards are generally less and the increased productivity benefits all participants.
DOGE on the other hand, is pointing to the corruption and misallocation of resources at the hands of the proponents of public spending.
In a word, no. The two concepts are diametrically opposed. Maybe things will shift in the future, but thus far they have focused on cutting. Hope this helps.