Maybe. But I would rank a fair few choices as more likely than Reed, top among them Kaine and Sebelius.
I'd like Warner as VP, but Kaine is just a weak imitation. And I'm not sure Sebelius would be the best choice being from Kansas, though she is far more popular at home than Kaine is.
If Obama is looking for a female to help him be competitive in the maximum number of swing states, I'd look at someone like Janet Napolitano, who might give Obama a chance to win New Mexico and Nevada (which would otherwise be in the McCain column).