I'm pretty sure you need access to the ToAU zone to do the quests. Once it's unlocked, you can probably play COR on a client without ToAU if you zoned in a zone your client has access.
However, to access the ToAU zones with a charactere, you'll need to register ToAU for that Account, Same way Rise of Zilart, and CoP had to be register. So in order to unlock the jobs, you'll have to buy the game :p
You'll prolly get a message when getting in FFXI that your account has ToAU but not your client and that some feature of ToAU won't be available to you.
That's what happens for CoP. When I log on PS2 for mulling I get a message that CoP isn't install.