Does rugby have any popularity in the United States?

Limited, mostly in your larger US cities and near large universities (the problem is that with the "big four" team sports, plus soccer, plus individual sports you're looking at a crowded landscape). It's "slightly" bigger here in Canada but still falls pretty low in terms of coverage. There is a North American rugby union comp (Major League Rugby) that has operated for two years and is expanding next year into DC, Atlanta and Boston (they have a team in Toronto that has a smallish footprint), and the Rugby World Cup that starts in September will get coverage (according to World Rugby's website, NBC/Universal has the US broadcast rights, but with time changes being what they are, if you want to watch most of the games will be late night/early morning).

If you weren't aware, Mark Bingham was a gay man who played rugby and is considered one of the individuals who was on United flight 93 on September 11th. Every year the Bingham Cup is contested among gay rugby clubs (some exist in North America). Gareth Thomas (from Wales) was one of the first male team sports athletes to come out during his career (he's captained Wales prior to coming out).

Here in Toronto Muddy York RFC is "open to all" and has a long history of being open to GLBTQ+ players. From what I can gather (they formed after I was done playing) they're doing a decent job recruiting university grads and recent immigrants who've played the game.

The USA Eagles are a sleeping giant of international world rugby union, I've said it for years, if ever they took interest and put money into it, they'd become a force, they have the athletes, athletic skill and talent and population.

Go Boks! Its no a major league sport in the US. There are leagues but they aren't covered by the media at all. I'm a Springbok fan, and I haven't been able to see a game in years.

It has some in some regions. Glendale, Colorado, for example, is known as Rugby town USA.

I don't think anyone really knows what it is in the USA.