But OP was wondering if there would be an issue with booting, not the activation (but that is still something to keep a watch over). Which it wont be an issue, that is what I was getting at.
I've never had an issue swapping either an OEM or manually activated windows drive onto another system with completely different components. Frankly I do it all the time, though I will admit it can cause a rats nest of software bugs, so your method is a clean and proper way of doing things when installing new components, though I am saying the computer will still work just fine.
Both aspects come into play.
Licensing/activation, and simply booting up.
I've had it fail completely upon seeing new hardware. Simply fails to boot up.
Sometime it works, sometimes it fails, sometimes it works...sort of.
Your "rats nest of software bugs" falls into the "sort of" world.
There is no "100% it always works".
I wish it were so, but
direct experience tells me otherwise.
And, given the ancient components and probable age of this system...how much old gunk is contained in that existing install?
Don't drag all that gunk into the new system. Start fresh with the new hardware.