Compared to ingestion, intravenous will greatly speed up the increase of methemoglobin levels. But it's a bad idea if you were to ask me. Injecting a solution of SN and water in the blood can lead to serious risk. SN is a salt, together with water, it will disrupt the fluid and electrolyte balance in the blood. Drastic changes in osmotic pressure may cause blood cells to burst or collapse. Dilution of electrolytes, can cause brain swelling, seizures, and potentially fatal brain herniation. Fluid overload from excessive water can strain the heart and lead to multiple organ damage and failure.
This could only work if SN lethal dose is very small, to a point where only little amount of solution will be administered via IV to do the trick.
I'm not sure why you're detailing this. You pretty much said, SN is going to kill you, so don't take it.
IV would be much more controlled than orally and all of them symptoms as
@MapleS rightfully asks, would kill you anyway; in fact, even quicker too.
You bypass the delays of GI absorption and enter the bloodstream straight away. Methemoglobinemia would occur immediately and you'd probably be unconscious and dead within minutes from how rapid the systemic hypoxia would be. Even then, all the listed effects of hemolysis, brain swelling, seizures, fluid overload, organ failure, are just mechanisms that will accelerate death. Cerebral edema or brain herniation will result in a rapid loss of consciousness and fatal brain compression. Funny enough, I imagine that is going to occur before hypoxia even fully kicks in. They're catastrophic medically and hence brilliant for suicides.
You will eliminate incomplete absorption for whatever genetic reason or from vomiting. You're pretty much ensured a lethal death with borderline no delay or uncertainty.
I am guessing Hiro Uchiha searched the dangers of IV SN and called it a day...