I think if you come to the Lane or to an away game, and you make an effort to interact with people, learn the songs, learn about the culture, learn some of the language (obviously not a problem for you as you're American), show respect and get behind the team, then 90% of people at Spurs will accept you as "one of our own", wherever you are from. A lot of people who come from abroad (these days) are tourists rather than genuine fans. But we have always had lots of fans from abroad who are proper as well. Always been a big link to Scandinavia and Belgium, some other places too, I've met Spurs from Serbia and Russia on our European trips, and I know there are some good lads from the US on this forum, as well as from other places.
By the way, I am English and live walking distance from WHL, and I feel the exact same way about the English national team as you do.