Each sex has its own privileges and burdens.
Perhaps one might slightly rephrase the question as:
"Do (wo)men have any *form* of systemic privilege due to their gender?"
I think the question can be tricky for males especially because all of the customs we learn from our patriarchal society seem to be in women's favor. However if you look deeper, women aren't actually benefiting from ideas that treat women as always nurturing, fragile, etc.
I'll this one out. I do think women have a few systemic privileges, but I also believe they are much more often on the losing side of it. So do they have any? Yes. Are they net-privileged? Hell no.