I do not understand why students keep thinking that their sexual orientation is a meaningful metric in college admissions. It is not. AOs really, truly are not interested, and I have yet to see / hear of any college saying 'we really want to attract more LGBT students. IF your essay helps it will be because you have written a strong essay on an over-done topic- NOT because of the topic.
re: Georgetown: you have a good shot- but prepare yourself for a deferral. Georgetown is explicit that there is no admissions boost for EA, and they use EA to admit the students that they really, really want- students who are such strong applicants that they likely to have better options.
Good luck 