Just gonna drop in :3
The dome that housed the Palintir was destroyed in 1437 Third Age.
The server is set in September 22nd 3001 Third Age.
That is a difference of roughly 1,564 years.
When something becomes buried it depends largely on 3 things: Weight, Weather, and Time.
The palintir (some of them) were large and required great effort to even move, others were very very small. The weight of the Osgiliath Palintir was described as being too heavy for one man to carry. Therefore, as you can see, one of the things you take into consideration is weight. This thing, while not overly large, was heavy. When something heavy falls in water it does not just simply sink to the bottom and rest, it buries itself in sediment.
If you want a comparison over how "hidden" something like that would be, take a look at this.
That is a box of, you guessed it, buried treasure. Its around the size of the Osgiliath Palintir but more importantly, the weight would probably be similar. Notice how it is half buried in sand.
Now lets move on to factor 2. Weather.
The Anduin is the greatest river in Middle-Earth. Its waters, while not rapidly flowing, are constantly moving. This isn't like the environment of the ocean floor where currents don't play a huge factor due to the depth, this is a river. Something that is constantly moving.
Constant movement = ever changing riverbed.
Ever looked at a rock on the bottom of a river? Every come back a couple days later? I can guarantee you that it would be covered with sand within a few short days.
So again, 1,564 years of sitting on the bed of a river. It almost certainly was probably 1/2 buried to begin with due to the impact of its weight. That thing is going to be buried.
Which moves us into the final factor: Time.
This is an object, of significant weight. Sitting on the bottom of a river that never stops moving. And its been sitting there for 1,564 years.
Years....
Not days, not hours, not minutes. Years.
The palintir would no doubt be covered in at least 5-20ft of sediment (1.5m - 6m). That is enough for it to never be seen. That is a depth of 2-6 minecraft blocks.
Now, it would be all fun and games to be touring someone through Osgiliath and go "There, roughly, in the river is where the Palintir sits after the Dome of the Stars was destroyed."
But to actually go down in the river and be able to see the thing? No.
Sure, they didn't have scuba gear or anything in Middle-Earth, but again, I reference actual history to backup my claim here:
The Nemi ships built by Emperor Caligula were sunk and lost for around 1,800 years (just a bit longer than the Palintir of Osgiliath). The area in which they were lost became a lake, and as early as 1400's people were attempting to raise them and recover the wrecks. Because they knew they were there (much like Gondorians would have KNOWN the palintir was in the riverbed).
They would, and I quote,
"often using grappling hooks to pull up pieces, which they sold to tourists."
If mankind knows something exists and it is there, we literally find and invent ways to achieve our goal of getting there. If the Palintir was easy to find, it would have been found. Simple as that.
So no, either it would be buried to the point where it could not be seen to be accurate. Or don't even bother putting it in the river at all because nobody is gonna be able to see it anyway.
- Phe
Tl;Dr : The shit is buried deep, nobody is gonna be able to see it. Either bury it like its supposed to be, or don't even put it in the river.