Alright, real talk from someone who powered through 'A Court of Silver Flames' in one sitting. No, Rhysand doesn't die in the main series. He gets close a few times—I genuinely thought Maas was going to pull the trigger at the end of 'A Court of Wings and Ruin' during that whole sacrifice bargain—but he makes it through.
What's wild is how many death fake-outs the guy racks up. The Cauldron in WAR, the pregnancy complication in 'Silver Flames'... you spend half the series holding your breath. I think it's a deliberate choice to keep the tension sky-high without actually offing a cornerstone character. After a certain point, you start to feel a bit immune to the threats, which maybe isn't great for suspense.
He's alive and ruling Velaris, last we saw. Whether that changes in future books is anyone's guess, but for now, the Bat Boys are all present and accounted for.