you're on the right track, forming the NH4+ COO- salt does occur, but if you try to concentrate that you are going to promote NH4+ COO- -> COOH + NH3(g). once you've protonated the carboxylate, you will form the final zwitterionic form of the amino acid (and that amine isn't volatile, so the same situation doesn't occur). this isn't just a theoretical situation either, it finds great utility in preparative anion exchange chromatography, where you elute with ammonium bicarbonate (or triethylammonium bicarbonate), then freeze dry down your fractions. the salts break down under vacuum to the amine, water and carbon dioxide (all volatile under these conditions), leaving your (involatile) compound.