In the books? Absolutely, because that is how the story was written. They didn't do anything to break that secrecy. That's the whole point of him having built a secret army. It was secret.
In the show, there is no established time of when or how long Orcs have been mustered in his absence. The timeline is compressed, and things are being pushed forward in some parts and not in others. Like, do you know where the evidence of the earliest Orc attack in the show actually comes from? Halbrand and the shipwreck survivors. And we don't really know how long ago they would have been attacked, since they never elaborate how long Halbrand had been at sea for or how far they had sailed after they escaped Orcs. Hell, we don't even know completely whether he is lying or not for that fact, since his entire background story is sus.
You could be right that Adar is acting on his own and not allied with Sauron at all. The problem with that explanation is that it would undermine the tone of the first season's premise - which is finding evidence of Sauron's return and the plot to create Mordor. If this side story were a massive red herring that amounts to nothing relative to Sauron, then it's a complete waste of time. Make sense? Like you could literally remove this entire sideplot if it doesn't have anything to do with Sauron's actual plans.It is only important as a location for a main characters story. It hasn't been shown to be a special place of magic to attract Sauron, Orcs, and Rings. It still hasn't even been made clear that Adar is currently allied with Sauron. Remember some orcs refused to follow Annatar. It is silly to claim it has been elevated to anywhere near the rings being forged in the story.
The context of the main plot of the first season is what we're discussing here. The watchtower arc already feels like filler. If you're then explaining that this could be a completely separate and unimportant thing, then this is exactly what I mean by comparing it to Chekhov's gun. It's about making a point that this would be unimportant to the main plot. It would be a sideplot that could be omitted completely IF it does not somehow tie back to the main plot in some significant way.
And frankly, I would have similar criticism of the Harfoot plotline seemingly going nowhere either, but it's way too early to tell what they actually intend to do.