Your warm feelings about it notwithstanding.
Given that these are employment figures, it's odd to segregate one career from all the others.
Otherwise, anyone can steal $18 trillion from the masses under the pretense of using it for the public good - when really all (yes, 100%) it does is pay debt interest according to the government's own report on how tax money is spent - and "create" several jobs for you as well.
So no, those shouldn't count unless you want to keep on living on fantasy land, believe government's inflation numbers (and close your eyes when you go grocery shopping), and ignore the fact those government "jobs" do not make us more competitive to other countries. You don't win in the global economy by giving everyone jobs, but by allowing people to create real jobs that compete with other countries so that we as a population become wealthier.