Thanks for the tip, both the popular and scientific article are interesting.
Short summary of the pros and cons:
- 
energy density: 3 x better than lithium ion
 - 
power density: really poor (if they raise their power density by 10 times, it will suffice for cruising, takeoff will require supplementary high-current batteries)
 - 
exhaust: sodium oxide (caustic), converted by moisture in air to sodium hydroxide (caustic), converted by CO2 into sodium bicarbonate (harmless) --> this is a tech for cruising up high, not for takeoff or flight above settlements ("don't stick unprotected head into exhaust stream, risk of losing eyes")
 - 
climate impact: positive, removes CO2 from air
 - 
operating temperature: reasonable (about 100 C)
 - 
mass production of sodium: doable, but somewhat messy
 - 
fire safety: sodium burns just as bright as lithium, nothing cheerful here
 
My personal conclusion: currently, this is a potential military technology ("electric cruise missiles / strike drones with 500 km range"), likely won't reach passenger or cargo aviation soon due to lack of sodium handling infrastructure.