Protein precipitation will produce a solid that is either denatured protein or a protein precipitate. The latter is the one pursued when adding salt. Nonetheless if the process is run rapidly protein denaturation will occur. There are several theories that try to explain what is happening. As you say as water is removed to increase randomness, the hydrophobic residues can now interact among protein molecules, if this process is fast once the protein molecules hit each other they will expose more hydrophobic residues that end up in a denaturing situation. You want this hitting process to be as soft as possible such that no new hydrophobic residues are exposed and only the native ones interact. Hope this explanation helps.

Thank you sir, it is more clear now :)

Not all salts are equivalent with respect to protein precipitation. They vary in the degree to which they are chaotropic (denaturing). Ammonium sulfate is used for preparing precipitates of active protein because it is unlikely to denature the protein. NaCl is somewhat chaotropic and is therefore not used for this purpose.