Sure I would, if the offer was not appropriate to the level of my mathematics. This lack of confidence does not come about by chance. Many women have faced a lifetime of suspicion about their talent, their commitment to work, their credentials. Badly, unless they join a group that wants them and wants to take advantage of such a slot as a gain to the group. Thus the solution is much more up to the group than to the individual, and there is where education is needed.
Senior women can make a difference.
For instance, by not frowning at special programs for women, but taking advantage of them and, thus, making them acceptable, and even desirable, for younger women. Let me, through an example, be specific here. In 1982 the National Science Foundation started a program of Visiting Professorships for Women in Science and Technology, which yearly sponsors a score of women to visit top institutions. This program highlights the existence of women scientists in places where there are few or no women faculty. It has enabled, for instance, outstanding women engineers working outside academia to teach engineering students who had never encountered a woman engineer before.