Since we're all (or atleast, some of us are) working with the benefit of anonymity, I would like to ask the hiring managers: if a candidate lists himself as gay and your workforce has a deficit in diversity, would it increase his chances of getting hired?
I do a lot of hiring of coders. Even though I like diversity and love getting applications from people that doesn't fit into the standard mold (white 20-35 straight male), I would not like getting it stuffed in my face.
Seeing someone listing being LGBT in a resume would kind of make me think about if that person expects special treatment or expect being hired because of a diversity goal. Basically, being LGBT would be positive when you apply to me, but being too forward about it would negate that positive.
if a candidate lists himself as gay and your workforce has a deficit in diversity, would it increase his chances of getting hired?
No. Personally I'd be a little worried that you are going to against me. It would not be the first time I've seen people come back with "you know I am <minority/> which is why you rejected me".
You are asking a very speculative question, whose answer varies with each organization you are applying and within that organization, with each hiring manager you are interviewing with.
What increases your chances of getting hired are your credentials - work experience, skills set, education - your attitude and the persona you project, where your persona indicates how well you will fit into the position and with the company. No matter who you are and no matter what what you are. For example, you certainly don't want to project an "I don't suffer fools gladly" persona if you are going for a customer facing position.