I will be upgrading from my current setup which is an i7 875k with the Gigabyte P55M UD2 motherboard to the i7 4770k with an H97 motherboard. Will Windows 8.1 boot correctly if I just swap out the new ...

It’s the end of the line for Windows 7 and Windows 8.1. These older versions of Windows (plus Windows RT) stop receiving all security updates today, over a decade after their original releases.