A capacitor of capacitance C is being charged by connecting it across a DC source along with an ammeter. Will the ammeter show a momentary deflection during the process of charging?

Yes. Ammeter shows a momentary deflection during the process of charging because charging electric field produce displacement current between plates of capacitor. The resulting continuity of current in the circuit is because the magnitude of electric field and charge over an area of capacitor plates is constant. Current inside capacitor ID=ε₀dΦE/dt