Yes but if the Ba'ku settled on that world before the Klingons claimed that space they aren't tresspassers.
Prior to the Klingons, the Romulans possessed the area.
From the wiki article you presented.
In Cone v. West Virginia Pulp & Paper, the United States Court of Appeals for the Fourth Circuit held that Cone ... because his actions did not change the land from a wild and natural state.
So, by this the Baku might have been able to establish a legal claim to the one valley they were occupying, and area where they built the reservoir, but not the entire planet, and certainly not the rings.
And what really works against the Baku in term of "adverse possession" is this.
The disseisor's use of the property must be so visible and apparent that it gives notice to the legal owner that someone may assert claim, and must be of such character that would give notice to a reasonable person.
The Baku, by their own admission, were hiding. That's part of the reason they choose a planet in the brier patch. According to the series Enterprise, when the Baku first landed, the area of space which included the ring planet was the possession of the Romulan Empire. Did the Baku make themselves "visible and apparent
" to the Romulans? No they didn't.
As pointed out by Edit XYZ, neither did the Baku make themselves "visible and apparent
" to the Klingons subsequent to the Klingons acquiring the area.
And later they didn't make themselves obvious to the Federation when they
acquired the area.
In the episode Spectrum of the Gun, when a Federation starship "encroached" on the space of the Melkot, they were met by a device that inform them of the Melkot's claim to the space. The Baku arrived at the ring planet by (presumably) a starship, and they were able to diagnose the exact problem with Data's positronic brain.
For them to have placed a reasonable number of buoys of some sort outside the brier patch to announce their presence and their claim to the ring planet would have been within their means.