Is it possible to have a diatomic molecule of sodium in gaseous state?
According to molecular orbital theory, disodium should be stable in the gas phase, with a bond order of one. The molecular orbital diagram is the same for all the alkali metals since they all have one valence electron in an $s$ orbital.



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NIST chemistry webbook has a small page on disodium and quotes an enthalpy change of formation of $142.07~\mathrm{kJ~mol^{-1}}$ which is moderately endothermic.

This page has a brief discussion of alkali metal dimers and claims that they are all stable in the gas phase, in agreement with the prediction from MO theory.