The answer is yes, provided they are qualified and have the right ideas. A woman like Hillary Clinton or Nancy Pelosi would take the country in the wrong direction and cause more harm than good to the women's movement.
I recall during the reign of the Clinton administration, whenever anyone criticized Hillary for her ridiculous attempt at nationalizing the health care system, or whenever anyone criticized her for her numerous ethical lapses (Whitewater, Castle Grande, cattle futures trading, Travelgate, selling pardons, etc, etc), some pundit on the left would attack the criticizer and claim that they were "afraid of seeing a woman in power" or something to that effect.
So where are the pundits now that Sarah Palin is being savaged? The answer is that they could care less about Hillary's or Sarah's gender. The left were engaging in gender baiting in order to pursue their political agenda. Peter Brown has some interesting thoughts on the subject:
This election will go a long way toward settling the question of whether groups that purport to speak for American women really do, or merely represent a narrow band of those who tend to be politically active, upper-middle-class and left-leaning.
It is worth remembering that Hillary Clinton got about 10 million votes from women in the Democratic primaries, but expectations are that roughly 62 million women will vote this November. Most of those 52 million are among the majority of American women who shy away from calling themselves feminists because they see it as having a negative connotation, and most of those who didn’t vote in the primaries tend to be more moderate and less interested in politics.
The fact that Gov. Palin doesn’t come from Washington, D.C., New York, Los Angeles or San Francisco; that she didn’t go to an Ivy League school; that her husband works with his hands; and that she has family problems to which many of these 52 million can relate on a nonpolitical plane makes her attractive to them.
Much more so than Sen. Hillary Clinton or House Speaker Nancy Pelosi, who are now the country’s highest-profile women politicians. Their views, values and way of life could not be more different from those of Gov. Palin.
If Gov. Palin becomes Vice President Palin, the clearly political National Organization for Women, the National Abortion Rights Action League and Planned Parenthood, as well as a host of other officially nonpolitical but left-leaning women’s groups, have a problem.
How could such groups and their political allies claim to speak for American women when the country’s highest-profile female politician represents everything they don’t?
Sarah didn't go to Wellesley and Yale like Hillary, she went to the University of Idaho. She and women like her don't call themselves feminists because feminism is primarily a philosophy that demonizes men and advocates legalized discrimination against them.
The nomination of Sarah Palin for VP has been met with enthusiasm among Republicans, Independents, and even some Democrats. She is even more popular among men than women. This has exposed the left's ridiculous charges of sexism to be nothing more than cheap gender-baiting.