Yes, there is mild vibrato in
LOVEppears and it becomes a little more prominent in
Duty. It's definitely more audible in her
I am... album. However, you can certainly hear it stick out in the
H single (I can't remember any vibrato in Free & Easy...). So, I'd say 2002 is where it REALLY started to become quite... "obvious," for lack of a better word.
And yes, as everyone else said: Voyage.
Ayumi is certainly capable of a natural sounding vibrato. I can hear it in her voice.

But I guess she just likes to (over)exaggerate it. lol XD