Personally, I wouldn't take the chance. While I know of many great females and of females getting along with other birds, it's generally birds of the same size. As Kathy pointed out, female Ekkies are hardwired to be more aggressive and to defend their nest sites. Eclectus are matriarchal, which means that the female is the dominant sex, not the male like in many animals and most birds. They also don't breed for life the way many other parrot species do. In the wild, males hop from nest to nest mating with as many females as possible. Another very interesting thing about Eclectus is that they don't have a set breeding season and tend to breed year round.
I have a male...had two of them up until June of this year. They were always as sweet as can be, almost never bit, but would defend themselves if they needed to against the other birds. I have a very stong willed Timneh grey who likes to cause trouble and the two Ekkies liked to gang up on him every now and then...it was kind of fun to see him get beaten at his own game every now and then. For the most part though, my males were/are the most docile creatures I have ever met in my life. Cooper, my remaining boy, just turned 8 in September. My biggest complaint about him is he can get very loud when he isn't happy about something and that usually involves me handling his current "girlfriend" Amarillo DHYA. I'm torn about actually getting him a female friend or possibly another male friend, another Ekkie. He was diagnosed with an unremovable mass in his lower abdomen this last June and I don't know how much time I will have with him. For now, he seems to be doing very well though.
They are amazing birds. I find the diet hard but I might be dealing with other issues (the mass). My males are/were just wonderful guys and downright loving to me. Taco, the one who passed away, was completely in love with me and wanted only to feed me and mate with me whenever he was out...that grew a bit tiresome
. I would definitely recommend a male over a female with a smaller bird though....just for safety reasons if nothing else.