I say, and with God's success: It is permissible for him to eat, drink, and sleep in the mosque; because fulfilling these needs does not contradict the mosque, even if he goes out for them, it does not invalidate his i'tikaf. Refer to: Al-Wiqayah p. 245, Al-Mabsut 3: 118, Al-Tabyin 1: 351, and God knows best.