Aluminum/Magnesium alloys can burn quite nicely. The stoichiometry is favoriable. Instead of $CO_2$ which is mostly oxidizer by mass, you might end up with $Al_2O_3$ and $MgO$ as exhaust.
However I can't imagine any possible way to actually cannibalize the structural material of a spent stage and then burn it. One problem is that the metal oxides of the exhaust are basically "ceramics" and even at very high temperatures they might agglomerate into nanoparticles, basically "glass soot". They'd be hot, but there may be little gas or volume and therefore little pressure and therefore little thrust.
Has this every been considered & written about in any semi-scientific way?