Was the Persian Empire driven out of the Indus River valley by Magadha?

There are several eras of Magadha - if you are asking about the Maurya Empire, it was established as far as the Indus valley by 322 BCE, by which time the Persian Empire had been taken over by Alexander the great's Macedonian Empire which itself had already unravelled in the east by the time of his death in 323 BCE.

So no, the Persian Empire had ceased to exist by the time the Mauryan Empire took over the Indus. Alexander was fortunate his soldiers refused to go east into India as he would have run into the overwhelming power of the expanding Mauryans and been exterminated.