You should most definitely not house them together! You'll have to quarantine the new bird before letting them in the same ROOM, let alone the same CAGE, anyway. My lorikeet annoys my cockatiels to no end. She never stops chasing them around, jumping at them and hopping around them... for a quiet cockatiel it can be pretty stressful. My lorikeet has hurt my budgie before too- they can be overzealous when playing.
Eg.
Note cockatiels posture and expression:
This explains itself!
