No government does not shuts down but people including those working in CIC going out to cast votes running draw will not be national priority.Why does the gov shut down next week for elections? I always believed elections aren't a reason for anything to stop .. but maybe Canada is different.
The focus will shift besides Draw requires Ministerial Approval which is formality but before next Wednesday there is a possibility that who is post election minister for immigration is not clear incase incumbent liberals are unable to make government by themselves e.g. Short of required majority numbers.
Also possible, Conservatives can come up on the top or liberals might end up requiring small parties support to form Government. This would means a week of uncertainty of who the Minister for Immigration is and conducting draw might be least of their concerns. Besides I think if they plan on having another draw liberals themselves would want to do it before elections but then again they could care less.