I would say no. The act does not specifically envisage privilege because it's not specifically described, but the fact that the information that is requested when the House is advised...we appreciate and realize it is covered by privilege, so that's essentially what starts the process, if you wish.
Even if a process was put in place by the committee for how to deal with a specific request, the point would have to be made that the documents always continue to be covered by privilege.
What the committee or the House ultimately would be doing is agreeing to the release of the documents, even though...and I guess that would be some sort of a caveat....