Upgrading hdd on old comp and re-install/activate windows

I'm going to have a play around with an old computer I have which is on its last legs.

I originally had an OEM version of win7 pro on there, then it upgraded to win10 pro.

I heard that these days I could change the hdd and just re-download win10 pro on a drive and would it auto activate because its the same motherboard? Is this true? I'm just making sure before I start lol