LOL,
As a person who was greatly involved in the "Gollum was a hobbit" debate I can only laugh at this topic. No, I don't believe that Frodo was gay, but you are not the first to suggest it. It has been suggested that The Lord of the Rings is homoerotic due to the lack of female characters AND the fact that the male characters bond awfully close to each other.
However, this is really a reference to World War I, which greatly influenced Tolkien's writings. During WWI it was only men that fought in the trenches and in the great battle while the women stayed at home. This is reflected in LOTR by how most of the female characters remain in their lands during all the battles. Yet Eowyn, by far one of the best characters in the novel, breaks from the tradition and eventually kills the Lord of the Nazgul.
There you go. Frodo is not gay in my opinion. But wait because TemplarLLM may have something to say about it. :P