For a strategy to be sufficiently not-luck-based, it needs to have a greater than 50% chance of meeting whatever damage threshold you put out. Whether Sleep Talk is choosing between two moves or three, the chance it lands on its most effective option is not high enough to meet that threshold, capping at 50% exactly if choosing between two. Short answer: I don't think Sleep Talk will help you.
Long answer:
Let's say you have a Choice Band Komala with Sleep Talk, Giga Impact, Superpower, and Knock Off.
Evil Incineroar knows you will click Sleep Talk, but he does not know which move you will select. He knows each move has a 1/3 chance of being selected. Given his priorities of Survive > Minimize damage taken, he will pick the counterplay option that causes him to take the lowest expected damage, assuming this option has a zero risk of him being OHKOed. We would conceptualize "lowest expected damage" as an expected value, an average, a mean. Let's work through a simple example to make sure we're on the same page when it comes to expected value.
Let's say that, for whatever unknown reason, Incineroar holds no item and changes to Tera Electric.
There is a 1/3 chance he will eat Giga Impact, a a 150 BP STAB move. We can factor in STAB to say it's equivalent to a 225 BP move.
There is a 1/3 chance he will eat a Superpower, a 120 BP non-STAB move.
There is a 1/3 chance he will eat a Knock Off, a 65 BP (no item) non-STAB move.
We can say the expected value / average / mean outcome is a generic move of the following base power:
1/3*225 + 1/3*120 + 1/3*65. Put this in your calculator to get an outcome of about 137. In other words, the "average outcome" here is pretty similar to taking a Superpower. STAB Giga is way stronger than non-STAB Superpower, 65 BP Knock is way weaker, and Superpower is exactly as strong as itself, so this outcome makes sense.
Let's return to our Sleep Talk, Giga Impact, Superpower, and Knock Off set. Learning how Evil Incineroar would respond here is a bit tricky and not obvious. For our math-loving friends, it's an optimization problem of the roughly the following form, where we need to minimize the following outcome. (The following form can be modified to be more generalizable to other situations.)
⅓*150*1.5*T1*I1 + ⅓*120*T2*I2 + ⅓*65*T3*I3
T(N) and I(N) represent the influence of Evil Incineroar's Tera Type and Item, respectively. This Tera Type and Item are the same across all three parts of the calculation – because Evil Incineroar doesn't know what move Sleep Talk will call, and because sets can't be changed after hitting the "Battle! button" he can't just prepare separate counter-sets for each called move and pick the appropriate one. However, the Tera Type and Item he chooses may interact differently with all three components of the calculation. Suppose he chose Steel as his Tera Type and Chilan Berry as his item. T1 = 0.5, because Steel halves damage by resisting Giga Impact, and I1=0.5, because Chilan Berry halves Giga Impact's damage. T2 = 2 and I2 = 1; Tera Steel makes Evil Incineroar weak to Fighting, and Chilan Berry doesn't matter here. T3 = 1 and I3 = 1.5; Tera Steel has no influence on Knock Off's damage, so it just multiplies by 1, and Chilan Berry makes Knock Off stronger by giving Komala an item to knock off.
For... various reasons... I will not attempt an exact calculus-based optimization and instead will present a reasonable, more intuitive guess on what Evil Incineroar might get up to in this scenario. Tera Ghost makes Evil Incineroar weak to Knock Off, but he becomes immune to the two strongest moves, so that's probably worth it too. Chilan Berry seems worth it, because halving Giga Impact's enormous power is more impactful than raising Knock Off's paltry power. However, because Tera Ghost nullifies Giga Impact anyway, avoiding Chilan is better to minimize Knock Off damage. In fact, because the only situation Evil Incineroar takes damage here is "eat a Dark-type Knock Off while Tera Ghost", the Colbur Berry is actually the optimal item because it will activate.
Given Evil Incineroar's tendency to minimize damage dealt, I will use my damage equation to see if this item/Tera combination seems like a reasonable guess for what he will do in this situation.
⅓*150*2.5*0*1 + ⅓*120*0*1 + ⅓*65*2*0.5
This equation sums to about 22. In other words, because Evil Incineroar is using the best strategy available, our Sleep Talk, Giga Impact, Superpower, and Knock Off set is about as effective as one hit of a neutral Bullet Seed. Clearly, our set is not a winner. But it gets worse. The only way this set does any damage at all in this situation is if it hits the ⅓ chance and lands on Knock Off. However, since its chance to deal Knock Off damage is less than (½ + 1), it is deemed too luck-reliant to count. The only damage threshold this set can hit without excessively relying on luck is... literally zero damage. I promise not all Sleep Talk sets will be this dismal and atrocious, but I don't think they will succeed.