Maybe? That depends on the exact nature of "indeterminism". Like a perfect libertarian free will that could have any thought imaginable (or unimaginable) would be indeterministic and unpredictable.
But for example you could also imagine something like playing a game of nim where you take turns taking 1 to m sticks out of a pile with n>m sticks and whowever picks the last loses.
Now the winning strategy is to start or set up the game to be n = m*x+1. So your opponent can have a perfectly free choice, you could hook up a perfect random number generator or let a god with free will play it, regardless of what they freely end up choosing, it ultimately makes no difference to the end result as you pick whatever is left to a multiple of m.
And if you can't imagine the strategy there's even marble computer version which does that "automatically". So despite the scenario being non-deterministic as it involves non-deterministic elements, the end result is still predictable with absolute certainty.
So this as well would have elements in it that are indeterministic, no knowledge of the initial conditions will tell you how many sticks they are about to pick. However ultimately it doesn't matter because whatever ends up being the result, will be the initial condition to a deterministic step.
Now the question would be really easy if we knew that this universe would be indeterministic, because then we could simply point out facts like idk a quantum experiment is like a coin flip, we can't predict the outcome of 1 experiment, but we can stochastically make good enough estimates about probability. So if an event happens on average 1 in 10000 times if we did a million attempts it's going to happen roughly 100 times and if we set up an expectation of it happening >1 there's a very high probability that this is true, not absolute, but really really close to 1.
However while there are occasions where despite seemingly indeterministic elements the result is really well predictable, there are other scenarios like chaos theory where despite seemingly determinstic elements the result is almost impossibly hard to predict.
So something being predictable or unpredictable is a necessary condition of determinism or indeterminism, but not a sufficient one so as we can't tell for sure what we're facing in the real world we can't even imagine a Laplacian Demon figuring we wouldn't know what he's seeing. If it is deterministic he would be able to use that, if it is indeterministic he would be as lost as we are, but we can't know either way.
This answer was written prior to the question being edited.
Under the Laplacian Demon any event would be predictable that is the point of this thought experiment. That if everything could be described as the classical mechanical movement of atoms or whatnot, all you would need is the position and momentum of every atom in the universe and you could theoretically compute any event in the past, presence and future. So in other words things would be deterministic.
You would still need computing power exceeding anything that the universe is capable of, therefore it's rather a demon observer outside the limitations of this universe that has to perform that calculation. But the idea is that if you knew all the relevant laws of how things work and all the initial conditions at 1 time frame you could predict everything that follows from that. And if the laws of the universe are as simple as movement of particles you could even go back in time as "the past" would just be movement in the other direction.
However that idea fails for several reasons. First of all not everything is this simple and there are processes that are non-reversible and where you cannot just go in the other direction. Thermodynamics and entropy for example. Suppose you generate heat via friction of a spinning rotator, however trying to reverse that process by spinning in the opposite direction, doesn't work it also creates heat via friction. Or there are quantum mechanical events where one experiment can have multiple outcomes. There's usually some statistics involved in that so while you can't predict the individual event you can predict multiple repetitions.
Another problem is that you simply can't measure the movement of the smallest things to perfect accuracy especially things like location and momentum can't be measured at the same time with perfect accuracy. And that's likely not just a technical limitation of our stuff but a fundamental problem.
And that inability to measure with perfect accuracy is not just relevant to quantum mechanics but also to chaotic systems. That is systems where a tiny change in the initial conditions has major influence on the end result. The famous butterfly effect, where something as tiny as the flapping of the wings of a butterfly happening or not happening could make or break a tornado somewhere down the line.
Or just look at this double pendulum:
And realize that something as simple as that can already become impossible to predict.
Now we can predict chaotic systems like weather for a few days and a biologist bird watching might be able to predict if a bird will land on that particular branch of the tree at that particular time (probably because they did so the day before and the day before that ...). But that would be making predictions of a very localized system that we assume is closed (even though we know it isn't), which we oversimplify and where our predictive accuracy drops very fast with time (events happening) and sorting out the past from what is, is often even more difficult.