It gets quite complicated.
The problem may arise particularly if the machine has more than one drive. The industry setup is often one drive with the operating system on and one for data. Older versions of Office stored the key in the registry on the same disk as the OS. You can install Office on either disk, in which case the key may be present on the other drive. (I think it’s different for the latest versions, but I haven’t checked. I think on M365 the key is linked to the account id).
I’d try it and see. If it doesn’t work, then you can look up removing the old key.
It maybe it recognises it as the same machine anyway. For example, Windows activation is quite sophisticated. It looks at several aspects of the machine to decide if it is the same machine or not before it re-issues an activation key. The idea is to allow for single component failure, like a hard disk, but pick up if it is different machine. It also depends on the type of key, whether it’s a retail key, volume license or MAK key etc. I would imagine Office may use a similar technique today.
@Kimberlin Yes, if you installed it on a completely different machine, you would need to de-register the original copy. You can do that through a Microsoft account, if memory serves.
