Yes, of course there are gay Catholics (including my ex-girlfriend, actually). From my observation, those individuals come to terms with the intersection of their faith and their sexual identity in different ways that are really personal. For me, I chose to leave the Catholic Church at about age sixteen for reasons along these lines before I came out to even myself (I find the Catholic Church's attitude on this issue to be incredibly inconsistent and hypocritical for various reasons I won't get into here but if you're curious we can talk privately about it). Others, I find, simply accept that their Church doesn't entirely support their romantic relationships (just like the millions of Catholics who get divorced or live with their partners before marriage or use birth control or whatever else); I can understand taking this position, but I am not sure I'd feel comfortable with it personally. And there are others who I think believe the Church has its own prejudices to deal with and who hope to encourage (slow) change from within. I'm sure there are tons of others who simply believe their sexual identities are sinful and shameful and aren't out at all.
It may be true that some of those people would want the Catholic Church to be legally forced to marry them if they want to be married, but I think (and this is a "from my observation" opinion rather than a "statistics indicate that" opinion) the majority would either accept, with regret, that the Church gets to decide that for itself, or would take the attitude of choosing to separate from an institution that does not accept them, at least when it comes to their marriage.