Gary Gates points to evidence suggesting yes:
Had LGBT voters not cast their ballots in Ohio and Florida, Governor Romney would have won those states. If the LGBT vote in Virginia had been less lopsided in President Obama's favor and more evenly split between the two candidates, Governor Romney would have also won that state.
All three states have sufficiently large LGBT populations to influence a close election, but none have sexual orientation or gender identity anti-discrimination laws nor any relationship recognition rights for same-sex couples.
(Image from the Williams Institute (pdf))