Do females always bowl wrap?

Will females wrap their bowls regardless of whether they've been paired?

Also, if you see a bowl wrap, is it generally too late to introduce a male?

All of my breeding females will bowl wrap, some more than others but they all do it "some" if they are breeding or have been introduced to a male.
Some females will do it even when not introduced to males, heck some males will do it also, lol.
Bowl wrapping helps them cool themselves during follicle growth, they will also lay on their sides or just stay on the cool side of their enclosure to achieve the same results.
It's only too late if the female has ovulated.