Premium time makes things easier and faster, but you can buy everything that provides an in-game advantage with in-game currency. So, as Spoon said, you don't have to spend a single real-world dime.
On another note, I unlocked the Yamato. She's amazing. But I find myself overextending and dying and very angry. Because if, say, those two BBs that are cowering two clicks behind me would just move up and contribute their firepower, I would still be alive. Or if that Khaba that is coasting 'round and 'round me would just use his bloody smoke after I specifically asked him to three times I would stay alive to nuke that Kurfurst and Amagi showing me broadsides, instead of being focus-nuked by the enemy team.
TL;DR: She's amazing, and she can take a beating. But, even though I want to take her forward and use that armour and 18.1 inchers at, say, 12-8km range, I can't because I get focused immediately, while my team discuss pie and cake. Must I snipe?