It depends on what sex the new bird is, and whether you put them in the same cage. If a bird is used to its own cage it might fight any intruders, alternatively, if you put them in separate cages they may pull their own feathers out with depression/frustration.
your parrakeet can only be pregnant if she is housed with a male, or has been in contact with one very recently. If she is pregnant she will lay an egg within 24hrs, however she may still lay eggs even if she hasn't been near a male but these will be infertile and wont result in a chicks.