Has "Don't Ask, Don't Tell" ever been challenged on 2nd Amendment grounds?

Some terms, mainly for non-USAians:

"Don't Ask, Don't Tell" is the current anti-gay policy in the United States armed forces -- the idea is that, while it's still not allowed to be gay and in the military, they're not supposed to make any attempts to find out whether folks are gay or not. It doesn't work very well.

The Second Amendment to the United States Constitution, part of our Bill of Rights (which is the first ten amendments to our Constitution), reads, in full,

"A well regulated militia, being necessary to the security of a free state, the right of the people to keep and bear arms, shall not be infringed."

Now, there are constant arguments about what, exactly, that means, but I think almost everyone agrees that part of it includes the notion that people have a right to serve in the military.

Has anyone attempted to challenge the exclusion of gays from the military on the grounds that military service is a right, not a privilege?