Sorta, but not like you explained it.
Romney could care less about social issues and because of that he allowed Obama to pick a couple of them to shore up support for his 2008 base. Abortion was never going to be on anyone's agenda in a Romney administration. However, Obama needed to make sure he kept as many women as possible, so he used that non-issue to drive a false wedge to stop any potential bleeding from the women's vote. With Romney being silent on it, Obama was successful in his fear-mongering and division to hold on to his coalition.
This was another example of how his lofty unification rhetoric is complete BS.