I would have to say that no, it's probably not healthy for parrots, and in fact could potentially be dangerous to them.
I could be wrong, but it is from my understanding that an ionizer can be dangerous to parrots over an extended period of time. This amount of time may vary depending on the bird, as it could be short exposure or long exposure.
The salt lamp also produces ions, so I would say it's better to be safe than sorry and don't use it.