Do they search for 'Rugby' though? America is pretty unique in the sense that most/all of their sports are referred to only by their main league names. They don't say they're going to go see American Football tomorrow or the Basketball. They say they're going to see NFL and NBA, even CFB - MLS, NHL - point is, they are in the habit of knowing sports by 3 letters only.
If we market as Rugby in the first few years to draw the existing Rugby fanbase in, then in years 3, 4 and 5 focus solely on marketing it as the 'NRL' and build that as the brand.
As long as they have all NRL related search terms on lock and key with SEO, so when someone searches 'play NRL' in the USA, an NRL based website comes up first, I don't see a problem with it.