No, it's not. Nami is a Tsundere, doesn't exhibit those traits. Tsunade is a tsundere, doesn't exhibit those traits. Touka is a tsundere, doesn't exhibit those traits. Rukia is a tsundere, doesn't exhibit those traits.
Not all tsunderes are like that.
I don't know about Nami, but those you mentioned aren't tsunderes in first place