I know that this is a very old thread. But I want to provide a better answer: I have a Ghelion's Demise with full auto and hand-laid stock. Very nice.

I've never seen it, no one has ever mentioned having it (except one person w/o their account linked that also claimed to have a Full Auto Perun's Fire... yeah, probably trolling) and it's not in the perk pools for any other Legendary Scout Rifle (VoC is special as its perks were set by Bungie.) Thus, I am inclined to believe that it is not possible to get Full Auto.

I'm curious myself