Would sodium explode in salt water?
Yes, sodium metal is also going to react exothermically with salt water or any other aqueous solution as long as it comes in contact with water:

$$\ce{Na (s) + H2O -&gt; Na+ (aq) + OH- (aq) + 0.5 H2 (g)}$$

eventually leading to explosion of hydrogen-oxygen mix forming near the water surface. Presence of sodium chloride in salt water isn't going to influence the reaction as it neither capable of shifting equilibrium to the left (gas formation), nor passivate sodium metal surface as it would do, for instance, some viscous oil.