Yes, all combinations of acids/bases are soluble.
First, if amide were acting as a base, it would acquire a positive charge, not a negative charge (add a proton to the nitrogen and calculate the formal charge). I would say the reason this does doesn't happen is because the lone pair on the nitrogen is already in resonance with the carbonyl function. This possibility of tautomerism gives the lone pair less of an incentive to grab a proton, especially in comparison to an amine, which lacks the immediate resonance stabilization available to the amide.