Is atom-clean aluminum active enough to react with alkali salts?
Even normal metallic aluminum (with its spontaneously-formed corrosion-resistant oxide coating) reacts with concentrated sodium or potassium hydroxide to give the aluminate (e.g. NaAl(OH)4), plus hydrogen gas. Lithium hydroxide should also react (lithium is likely functioning as only a spectator ion) whereas alkali metal carbonates may not be sufficiently reactive. 

This reaction is not what you refer to in your question as "substitution" reactions, where the alkali metal ion would be reduced to metallic form. Note that aluminum chloride is reduced by sodium or potassium metal to give aluminum metal, so the reverse reaction is unlikely to occur, but the energetics may be different for the hydroxides or carbonates in a non-aqueous environment.