I really don't see how. Sure, some characters might work better single, but I never had a problem with Supes, Spidey, or other characters being married. I'm not seeing the narrative interference.
I never cared for Batwoman, to be honest. I only ever read her in Detective's "Elegy", and as much I enjoy Rucka's work, it didn't feel particularly strong. But that's me. Playing a bit of Devil's Advocate, I suppose it's possible that DC just doesn't want a married hero right now (Besides Arthur Curry), straight or gay. They can't be concerned about backlash, given the X-Men married off Northstar (at least, it was less annoying than Storm's wedding).
I think perhaps what VS said is correct, a gay marriage in comics today, and all it symbolises would indeed inhibit storytelling.
If DC were to eventually do to Batwoman what they are currently doing to Animal Man, ie have he and his wife break up, they would be accused of homophobia, because gay characters in comics are so few that fans feel they have to be protected. There was an article on Comics Alliance yesterday where the writer was freaking out because Jason Aaron said Amazing X-Men would have a rotating cast, which could mean Northstar would lose prominence. Completely baseless hysteria, but because Northstar is gay, he is taken seriously.
With gay characters, you can't do anything interesting with them as characters, because of the gay. Look at the anger over Hulking and Wiccan breaking up.