Is iMessage tied to an apple account or a phone number? If I send someone a message through iMessage from my Macbook and they are to receive it on their iPad/iPhone, what will happen if that person has changed their mobile phone number since I added them as a contact?

Will they still get the message?

I initially contacted this person with an email address.
Usually iMessage is tied to the email associated with iCloud. If the person is using iMessage on their new number they would have logged in with their email address and hence receive the message.