Why, in the name of dog, would you ever want to keep running Win7/8/8.1? Go to https://www.microsoft.com/en-us/accessibility/windows10upgrade
and get the free upgrade (before January 16).
But to answer the actual question you asked, yes, all modern processors (and motherboards) will run Win7/8/8.1. You will eventually run into a problem with drivers for such things as GPUs, and compatibility issues with applications (especially web applications).