ThrashZone is correct. If you do a successful Windows 10 inplace upgrade ie click upgrade this pc (or click setup.exe on an install usb/dvd from within Windows 7) and it activates, then when all is OK you can reboot from the install media and do a clean install. After the 1st inplace upgrade, Microsoft stores your hardware info on their servers, so with the clean install, the pc will be recognized and activated. I have tested this clean install method on VM and real boxes. During the clean install, when asked for a serial you should click skip or ask me later.
BTW - just like a W7 serial is valid for x86 and x64, you can clean install x64 on an initial 32 bit W10 upgrade. I have also tested this -
Windows 7 x86 > Windows 10 x86 upgrade > Windows 10 x64 clean install
versions must be the same ie Home Prem > Home, Pro > Pro etc. You can't go x86 > x64 on the initial upgrade (but can with a 2nd clean install).