I doubt that it is metallic sodium, for the same reason why the rechargeable lithium batteries do not use metallic lithium electrodes like the non-rechargeable batteries.

During charge-recharge cycles, a metallic electrode is likely to be degraded quickly.

So it is more likely that the reduced sodium atoms are intercalated in some porous electrode, e.g. of carbon, while at the other electrode the sodium ions are intercalated in some substance similar to Prussian blue.

The volatility of sodium does not matter, because it is not in contact with air or another gas, but only with electrolyte.