Even before getting to protections under charter rights, one needs to look at the issue as a question of parliamentary law and whether these documents would be admissible in a court of law as documents obtained under the authority of a House order and are directly and closely connected to parliamentary proceedings.
Also, the House and its committees need to consider the potential impact of such an order. Witnesses come to committees and testify. They're told they have immunity while testifying. It will destroy the root of the privilege itself if testimony or documents were, as a matter of principle, referred to the RCMP once the evidence has been given—