The G.O.P or Republican Party does benefit from female support. I am not affiliated with this party and I don't share their values, but I do believe they would benefit from female support. This is because if other females see their same sex supporting this party, then they will fell more confident supporting it as well. That is if they are leaning towards the party already.
The GOP, along with every other political party, benefits greatly from female support. Female voters are a large and powerful voting group that cannot be ignored during any election. By catering to women, the GOP can gain thousands of votes. Solidifying its standing with this core group can have benefits for years to come.
Right now, people are accusing Republicans of not being female-friendly, due to their socially conservative beliefs on such things as abortion. That does not mean that the Republican party needs to change its stance on issues, but it does mean that they're being perceived by society as being mostly males who aren't in touch with women's issues. It would certainly help the party if more high-profile women would announce that they support them, so that this stereotype would go away.
The GOP does benefit from female support. The female support of the party softens its often hard line image on things and also attract more people that have potentially less radical views about things. Female support also encourages women to vote, and as they make up over half of the population, their support is needed.
I don't think there is a lot of female support behind the GOP. They wanted to not have the equal pay for women act pass, they are obsessed with women's health and abortion. They don't want some forms of birth control to be legal. I think that women who are smart do not support them.