I have a fair amount of experience with Amex Offers though not this one in particular. In my experience with hotel offers that often have geographic limitations (e,g. North America only) Amex is able and does enforce the terms. However, I found times where the terms are not enforced so YMMV. Basically unless you find somebody who has done this exact offer you probably will just have to try it yourself.

To answer you question on how they potentially know. One is who is doing the charging. With airlines you will often see different subsidiaries for tickets bought originating in different countries and two it is obviously going to be charged in GBP so that will be obvious to Amex's logic.