As far as I know, Bax Music is actually a Dutch shop, although they do have individual sites for some European countries as found on bax-shop.com.
Ordering download codes is definitely not an automated process. I purchased some download codes from bax-shop.nl a couple of weeks ago, and ran into a few problems.
For the first order payment was unsuccessful, even though the credit card payment process appeared to go okay. Immediately received an automated email with a link to try that process again, so that was quickly rectified. But then you're supposed to get the code on a packing slip that should arrive by email, except it never did. It then took several days for them to respond to my email inquiry.
A different software item couldn't be ordered without adding a physical product or the checkout process would fail with a "too many redirects" error. That code was indeed sent on a packing slip: by email, once the physical item was dispatched, and included in the package.
I don't know if I would recommend ordering from them with a "fake" UK/EU address.