Yes, an aqueous solution of ammonium carbonate contains ions. When ammonium carbonate is dissolved in water, it dissociates into ammonium ions (NH4+) and carbonate ions (CO32-).
The chemical equation for the dissolution of ammonium carbonate is:
$$(NH_4)_2CO_3 + H_2O → 2NH_4^+ + CO_3^{2−} + H_2O$$