At what saltiness will water simply pass through us?
"Unaffected" is impossible. If you meant homeostasis, where fluid ingested = fluid excreted, well that happens all the time, and all "output" is not through urine. Sweat, respiration, fluid in feces, etc. are fluid loss. The body constantly needs water. Fluid regulation is a highly complex system managed by the body through a variety of osmotic gradients in the body and hormones which is not driven solely on the osmolarity of the fluid ingested. Under no circumstances would fluid ingested pass through the stomach, small and large intestine, and colon without absorption. Once absorbed from the GI tract to the bloodstream, our kidneys regulate fluid balance. For more reading, reference the renin–angiotensin–aldosterone system.