Can magnesium sulfate (iv) relax the baby too much and cause important organs to fail?

Usually not. Mothers get Magnesium Sulfate at times to control her high blood pressure in labor & some passes into baby. Over 3 decades I have had babies many born with poor muscle tone & one that came close to needing breathing assistance. Their high magnesium levels begin to fall as soon as baby begins to make enough urine, usually less than a day. I have never seen or heard of organ failure from the magnesium.
No. In fact we have found that premature babies who receive magnesium have less bleeding in the brain. Magnesium should be used cautiously because it can have rare but serious side effects in the mother such as too much water in the lungs.