I would suggest probably not a SWAT team.
Daniel Lavoie represents Public Safety Canada and actually co-chairs that interdepartmental committee—with the Privy Council Office, in fact. The whole idea is to make sure that you have a common community of interest of senior officials who are sufficiently seized with the importance of emergency management, have credibility within their organizations, and can get these plans rolling and get action on the plans as needed.
When it comes to a response to a particular emergency issue, it wouldn't be an ADM committee. They may be involved in different parts of the response, but really, at that point you're looking at the locus of the issue, at who the first responders are, and making sure that they have support.