Real answer to the uninformed question.

I am going to try to anwer the uninformed question: "Will her gender sway women to Palin?" 

That misses the point completely.   The premise of that question is that there are women who are totally void of brain matter, see a woman and thus will vote for that woman.    That is absurdly insulting.

Women have opinions on issues that supercede their gender.   Let's take abortion.  Some women are for legal abortion and some are opposed to it.    Those who are for legal abortion are not going to be "swayed" to Palin solely because she is a woman.    Just like pro-life women would not vote for Hillary because she too is a woman.

The choice of Palin will indeed have a clear sway on people but the sway will not be restricted to gender.    Evangelicals, social conservatives, pro-americans, outside the beltway types (you get the picture) will be swayed because they finally see a product they want to buy.   There was a large group of the Republican base that was luke-warm to McCain (I am one of them).  We saw three U.S. Senators (Obama, Biden and McCain) on the ticket thusfar and felt that we were being unrepresented.  The addition of Palin, though I may sound melodramatic, finally included America in the race for the presidency.     Average, hard working Americans of every race and gender will see Palin for who she is and that she represents the America outside of Washinton DC.     That will ultimately "sway" them whether they be male or female.