You're right but Hillary never ran for anything prior to becoming a Senator from New York. No small feat. I don't think holding an elected office would be an issue in a Rice/Clinton race. I do believe that Rice would take away enough of the African-American vote to sink Hillary regardless of how much voter fraud the Democrats were able to pull off.
Lots of folks run for Senator as their first office and win, President is a different matter. And now that Hillary has that all important first win it's a non-issue for her. I don't think Condi would take a significant portion of the black vote, problem with the black voting block is that they believe strongly in the "uncle tom" concept, Condi has already been quite effectively given that brand, which makes her not black as far as they're concerned, and therefore she offers no inspiration to switch parties.