Speaking as a former 911 operator, I can say fairly certainly that a 911 operator won't object to you calling to try and access the poison control center. They'll probably just transfer you, OR (more likely, depending on the policies of the jurisdiction in question) go ahead and dispatch an EMS crew to your location.

I would think that the time saved not looking up those numbers yourself and just dialing 911 would make it worth always dialing 911.