Maybe eventually, but at the moment EVs are under tech pricing rules where there's early adopter pricing. New EVs are expensive because some people are willing to pay a premium to have the latest and greatest tech. While that's still happening, those people probably aren't going to opt for a sodium battery that won't have as much range. And for those wanting a cheaper EV and don't need as much range, they can save a lot more money by simply buying a used EVs.
EV batteries last a remarkably long time, most EVs made 15 years ago are still running on their original battery. I suppose those batteries will eventually start failing and so there will be a market for sodium batteries to replace the old lithium batteries. A new sodium battery would only need to provide the same range as an old lithium battery for that market.
So I guess yes, they will be used in cars. Replacement batteries at first, but my guess it will be longer before they're an option in new EVs.