No dice! She’ll take the deal and LIE on the record to cover for everyone knowing fully that her deal protects her from perjury.
The right approach here is to demand she pony up a proffer as a precondition of immunity. A proffer is a non-incriminatory statement, usually made through a lawyer, of what the witness is prepared to say under oath.
If she then lies under oath, breaking her proffer, the immunity deal becomes null and void.