Was Windows 10 pre installed on current PC?
Before you do anything, check in settings/update & security/activation
If next to activation it says Windows is activated with a digital license, then your licence is still attached to hardware. If you have a MIcrosoft account, you can link it to licence by slicking add an account button. If you don't have one, click this link and make one - https://account.microsoft.com/
If next to activation it says Windows is activated with a digital license linked to your Microsoft account, then your licence is currently linked to your email address.
To answer your question, NO, not if you can link it to email address. All you need to do to move it then is follow the steps under Using the...