It can be replenished through rest and nourishment and it grows through developing the mind and body, but yes. If I exceeded my limitations and used all of the chakra in my body, I would die.

[She pauses. Konan isn't about to share how much chakra she personally has, but she can share another tidbit of information about chakra in general.]

Most people are more likely to lose consciousness from depleting their chakra well before they're at risk of dying.