I tried using Shehulk's petrify debuff from SP2 to stop Doom's Aura from activating, it does not seem to be working. I haven't tried using petrify from other champs yet.
Shehulk's slow debuff works perfectly to stop the Aura from activating. 
Can one of the devs comment on this interaction please. 
Included a video below. 
https://youtu.be/nASNNGY7Wf4