It's a possibility. The south, especially TX, drag the national white vote down for Dems a bit. Bush only won white women by 1 point, and within the margin of error, according to exit polls for 2000. So Gore probably won them outside the south. Clinton definitely has a chance against Christie.
If Gore could draw among white women, then Hillary can surely win them outright.
People seem to have forgotten already how much more controversial a black president is for people 65+ than a mature white female president would be. The female suffrage fight was battled out 100 years ago, before 99.8% of today's voters were even born. While the civil rights fight of the 1960s, the white flights from the inner cities, the murders of almost all the main civil rights champions are still fresh in many mature voters' minds.