With accents, do perceptions vary by gender?

Sometimes, yes.
I’m from the south and I consider some southern accents to actually be very hicky as opposed to a sweet southern lilt. I don’t think it matters much with the gender. Hick is hick, no mater the gender.

Like @chyna said, it’s not the gender, but the degree of ‘hick’ in the accent. Of course, this is an incorrect perception as well, but I admit that my knee-jerk reaction is to think ‘hick’ accent = less intelligent. I know better, too! I married a very smart West Virginia man whose family has the hick accent. He ditched his accent back in his college days because of that very stereotype (though it comes out when he’s mad, which is kind of funny). Obviously, intelligent people come with all sorts of accents.