No, it isn't. For example,
here is a page from Armenia's government website (therefore written in Eastern Armenian) about the former president, Robert Kocharyan. You can see that the page spells his last name "Քոչար
յան".
In Western Armenian writing, the letter
յ does not even represent the sound "y", as far as I can recall, but rather the sound "h": for example, the Armenian equivalent of
Jesus is written
Յիսուս (with initial
յ) in Western and
Հիսուս (with initial
հ) in Eastern, but pronounced [hi'sus] in both.