I've had several pairs of budgies over the years. They never once produced eggs. Introducing a male to a female does not mean she will suddenly start laying eggs.
It is advised to keep male/female pairs over a pair of females, since females are more territorial and thus more prone to fighting with each other than a female/male pair would be.
"Because females are more prone to territorial fighting over space, it is less advisable to keep two females together. Female parakeets bicker more among themselves, stand their own ground, and their disruptive arguing leads to squawking beak duels that disrupts everyone." From
this website.