Their civilopedia entry says they can move on the same turn, so it is definitely intended. I play on epic speed and without any discounts a Landsknecht costs 300 and 220 with Mercantilism. I don't have Big ben, but Landsknecht will cost around 60% as much as a Pikeman, maybe a little bit less. I can afford to buy one every second turn. I don't think Arsenal of Democracy is such a big issue. You can still only gift units every third turn and by the times ideologies become available you'll have to upgrade them to remain useful. It's a cheap way to gain influence, but it's still a lot weaker than Treaty Organization or Gunboat Diplomacy.