Varys' text box is pretty clearly a passive ability. But, bringing him out of shadows is triggered or no? I am thinking he can't be cancelled by the Throne.
Lannister Iron Throne (LotR) vs. Varys (SaS)
Yeah you can't cancel bring a card out of shadows. and you can't cancel his passive ability. So no go here.
Bringing a card out of Shadows is not a triggered ability - any more than, say, declaring a character as an attacker or defender is a triggered ability. Game mechanics do nor count as card abilities.