No, not necessarily. The problem isn't so much the cpu cores, those will be mostly backwards-compatible. The real problem are all the other discrete PCI devices. If Microsoft does not provide updated drivers for their older OS releases, those older releases have no chance of working on newer hardware.
For example, Intel's Skylake chipset has I219 gigabit ethernet now (uprev from I218 which itself was an uprev from I217). The chance of older ethernet drivers working with newer chips is zero. In the case of the I219, the flash mapping and access mechanics changed drastically.
The integrated GPU is another good example. Skylake is up to Gen9. The chances that Gen8 code will work with it are zero.
One can go down the list. The only chipsets which are generic enough for older drivers to work are going to be the USB and AHCI chipsets. Everything else? Forget it.
But I don't know why people are complaining so much. The same can be said for BSD and Linux distros. An older BSD or Linux release is not going to work on newer systems. Most people don't care since they just update to the latest. While it is possible to backport the drivers to older OS releases, not very many people have the skill required so for all intents and purposes you need to run newer OpenSource OS's on these newer chips too.