Well, a lot of medicine is kind of centered around sodium and water management.
Your body has dual sensors for osmolarity (solute, mainly sodium) load and blood pressure. This is acheived through hormonal feedback on several axes, which work on blood vessels, your kidneys, your large intestine, and your brain (in stimulating thirst or seeking shade or other stuff).
Much of this is acheived through your kidneys, which can work to conserve sodium and can reabsorb water directly, through largely parallel systems. For the most part, water follows sodium, so if your body reabsorbs a sodium molecule, water will follow it to maintain osmolarity. So sodium reuptake will also serve to bring back water.
I’m gonna leave it at that, without talking about renin/angiotensin/aldosterone, ADH, different transporters in the kidney, etc. etc.
Pharmacologic diuretics generally work directly on the kidney, and modify how well they reuptake sodium or water. Other diuretics may work on simple osmosis. A good example is glucose in diabetics. When their blood glucose gets above 160 mg/dl, the glucose reuptake transporters in the kidney begin to become overwhelmed, and glucose gets left in the urine. This draws water into the urine to balance the osmolarity, and you end up with polyuria (lots of pee), polydipsia (lots of drinking to replace water) and glucosuria. Alcohol is partially a osmotic diuretic, but there is also evidence that it modifies one of the body’s blood pressure maintenance mechanisms, the ADH system. In effect, it tells your body that your blood pressure is too high, so you pee to lower it.
This is acheived by the second axis – pure water reabsorption in the kidney. It will dilute your urine no matter how concentrated your blood is. Therefore, you are probably not losing that much salt with drinking. Replacing salt in this circumstance would only serve to make your blood more concentrated. So the simple answer is that is won’t work.
There is a medical condition very similar to this. Sometimes, with head trauma or in some other conditions, ADH is not released or the kidney doesn’t respond to ADH. This is called diabetes insipidus – not related to “standard” diabetes, diabetes mellitus. It just (IIRC) is Greek for copious amounts of bland-tasting urine (not copious amounts of honey tasting urine like in diabetes mellitus). In DI, there is no concentration of urine and the blood can become dangerously concentrated.