Remember this is XIV, not XI.
Key word is *accessible*
It's highly likely you will be able to lv to 60, as soon as you register Heavensward, without having to do any quests.
It's like with Reaper of Souls expansion for D3, the disc contains a 2.5mb file, that doesn't really do anything, you don't patch the game; the normal patch to D3 already has all RoS content, but you need to enter RoS key, to get access to it. you cant level to 70 without RoS, even though there's not even any extra patch for it; you only register the key, then you have instant access to all RoS content.
I'm pretty sure that patches for ARR will contain Heavensward content as well, or you wouldn't be able to see mach/DK/astro ppl, or the equips they are wearing. But you'll need to register exp key, to lv to 60, and all that.