He will not
1. Unlike those who died, Shikamaru is not attatched to the Shinju tree.
2. When Naruto thought of Asuma, he had "..." in his panel.
3. Sakura is directly healing him.
4. Tsunade is on the way.
5. They need an actual strategy to win. Having just overheard this information, he'll likely form a plan when he is healed enough.