No, they’re almost entirely unrelated. Almost all CPUs will idle close to 0 W (with correctly working drivers). The main idle power contribution comes from the mainboard and other devices (e.g. disks). The Mini PCs you mentioned should have a very low total idle power, probably below 10W.

Check out Wolfgang on YouTube, he has some great videos on the topic: youtu.be/Ppo6C_JhDHM