OK - it doesn't work. If you sign in with the UK email address, it gives you the message on the right:-
You are signed in as
xxxx@gmail.com
Use a different Amazon account
This title is not available for customers from:
United Kingdom
Contact Customer Service to exchange for Gift Card
So you have to have an account registered on the .com site with the appropriate addresses etc to make this work.
I wanted this book anyway and it is cheaper in the US, so have accepted my own gift and now have to unregister and re-register Kindle4PC as I don't have any devices registered at Amazon.com any more since I moved to the UK site.
They'll need to clean that up as it wasn't that clear, certainly not for someone that is gifting items, they might not think to change the country thing to say UK or wherever.