No, current flows in balanced Wheatstone bridge because:
According to circuit diagram when bridge is balanced the potential at point B is equal to potential at point D. 
Hence two points are at same potential
		VB = VD
Potential difference across galvanometer is zero
                       V =VB – VD = 0
According to ohm’s Law current through galvanometer
		Ig = V / Rg
		Ig = 0 / Rg = 0
Therefore no current flows through the galvanometer and 
it shows zero deflection.

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