The answer to this is a bit more nuanced than a simple yes or no, as an Augury concerns a specific planned course of action rather than a question about an individual, and has four specific outcomes rather than specifically failing in some way.
The Augury spell description (PHB p. 215) says:
you receive an omen from an otherworldly entity about the results of a specific course of action that you plan to take within the next 30 minutes. The GM chooses from the following possible omens:
- Weal, for good results
- Woe, for bad results
- Weal and woe, for both good and bad results
- Nothing, for results that aren’t especially good or bad
The spell doesn’t take into account any possible circumstances that might change the outcome, such as the casting of additional spells or the loss or gain of a companion.
So the way this would play out is that the caster will outline a planned course of action and the GM will choose from one of the four outcomes not taking account of the change in circumstances represented by the existence of the character wearing the amulet, as they don't exist as far as the spell is concerned.
Some examples to illustrate this:
"We plan to kill X with a big magic flaming sword" where X is wearing the amulet. I would adjudicate a Nothing answer, as, as far as the Augury is concerned, nothing would happen as a result of the plan as the person does not exist, and so it is not good or bad.
"We plan to kill X with a big magic flaming sword" where X is personally vulnerable but has a really tough bodyguard wearing the amulet. I would adjudicate that the Augury would return a Weal answer as, ignoring the circumstances represented by the bodyguard who does not exist as far as the Augury is concerned, the killing should be easy.
"We plan to kill X by having Y run up to them and hitting them with a big magic flaming sword" where Y is wearing the amulet. I would adjudicate that Nothing would result as, as Y does not exist as far as the spell is concerned, the Augury will divine that nothing much will happen, which is not good or bad.
In all cases the GM simply ignores the change in circumstances represented by the person wearing the amulet, they simply do not exist, to work out the result of the Augury.
The specific scenario described in the question will ask if the plan to enter the cave in the manner described will work out well. You should answer as if the rogue does not exist, i.e. as if there is no ambush, no possibility the enemy will spot the ambush and no help of any kind will come from the rogue. This sounds like the Augury will answer if a straight up fight between the enemy and the party, without the rogue's input, will work out for them, probably a "Woe" or a "Woe and Weal", depending on the challenge.