Seriously, Canada has no such immunity for sitting MPs. If Justin Trudeau got charged with any kind of crime tomorrow, he'd be out of office before the end of the day, and a new election for his riding would have to be set up to replace him. It doesn't even matter if he's eventually found guilty; if he's not being prosecuted, he can run in the
next election, but he doesn't get his seat back, let alone the Prime Minister position.
The only real privilege MPs enjoy in this regard is freedom from arrest for
civil cases. If someone's suing you for $20,000 for breach of contract, the courts can't send police to cuff you and drag you to court. They
can still sue you, and the courts can find you in contempt for non-appearance and rule against you accordingly, though.
https://www.ourcommons.ca/marleaumon...Sec=Ch03&Seq=6
This is where the "strong civil service" comes in. You've still got star generals and admirals, right? There are, I presume, drafted plans for responses for invasion. The military can handle itself in that regard. They can't make decisions on attacking a foreign power, since they have no authority to
declare war, but they
can levy the full strength of the military in the nation's defense.
Same applies to every branch of the civil service. If there's no government, and no Minister of Health, nothing gets shut down. If it happened right now, our vaccine rollouts would continue, and continue adapting to new circumstances. The lack of an elected Minister means there's no capacity for the civil service to change their own mandate, but
serving their
existing mandate, that's not something the elected Minister is required for. Indeed, their input is often
unwanted, as they generally have far less experience than the senior professionals in the service branch.
An inability to shift policy
direction is not an inability to
effect current policy.