For some time, in Mavericks, I had an option, which I had disabled, in Users & Groups > Password to reset the password using Apple ID
This option vanished after a migration, under Mavericks, to a new machine
and remains absent after an update to Yosemite
So I can't tell: Can a I reset my password using my Apple ID or not?
I had explicitly disabled this earlier for security reasons, but now I can't tell whether it has been enabled or not (or how I'd change it if I wanted to).
Best Answer
Here is what is going on with missing reset password with Apple ID.
How to in FileVault is described here.
Since you are NOT using the Apple ID password recovery feature (it is not enabled) your FileVault password is NOT vulnerable to it. It can not be used on your system to recover your password.