A parakeet???? If you mean a budgirigar..... if it is in the same cage, yes. In an aviary, maybe not.
Eclectus parrots will be in breeding condition at the time of the year and will be getting a bit edgy, especially the female (hen).
Having said that, there are some pet Eclectus parrots that live in perfect harmony with other small birds. There is no one rule for animal behaviour. Common sense must prevail.