While it could kill Naga, I'm pretty sure that Naga can just cancel the ability entirely with Sykuria Shield due to a few factors.
We've seen Beerus transmute and egg into sand/dust, but when fighting Champa, they ended up turning a whole room to dust over the span of several seconds or so. Naga is far larger then either an egg or room like that, so I would assume that it would take time to fully transmute him into Dust.
Another point is that this ability isn't necessarily a conventional attack. Naga's Sykuria Shield is capable of cancelling out abilities and powers that aren't conventional, as well as moves that are conventional. This ability to transumute something isn't something with raw power behind it, so it'd likely not be able to cancel out the Sykuria Shield in the same manner that Drago did.
Essentially, I'm saying that it the actual process of transmuting Naga may be slower, due to how Beerus even took some time to turn a large portion of a room into dust.
Also I don't really recall a time where Beerus resorted to using this ability against someone when in battle, regardless of being serious or being casual, outside of Champa, in which it was just a side-effect of their clash, and it was not like he was actively doing so, it seemed. He kinda seems to just... Do it at times. But he usually just blasts things away if he needs to kill/destroy them. So chances are, even if he was bloodlusted, he'd stick with his other, more conventional attacks, which could be countered by Bottom Zero and Sykuria Shield and allow for Naga to win.
