where I hunt there are two rivers running through,we have taken many , many deer that went into the water.9 out of 10 will sink just below the surface.if you look close it looks like a small brown bowl at the top of the water.most times if you don't get to it in a few min. then it will go down.shot through the lungs with a rifle or shot with a shot gun with buckshot, it will sink almost immediently. that 1 out 0f 10 will go down like a rock. I have saw this many times. we have even had a guy take his scuba gear and find them for us 10 to 15 yards from where they went into the water.
I guess it all depends on how the deer was hit.