Boost regulator: Using inductors with greater value than datasheet suggests to improve performance?
Maximum output current is primarily determined by the current ratings of the switching FETs. Increasing inductance will only slightly reduce rms switching current due to lower ripple. So you could use a 20uH inductor, but it wouldn't significantly increase the maximum output current.

A more important factor is the physical size of the inductor. A 20uH coil with the same physical size as a 4.7uH coil will probably have around 4 times higher resistance and 4 times lower saturation current. Higher resistance causes greater loss. Lower saturation current causes higher ripple (sharply increasing as peak current approaches saturation). Both result in lower maximum output current. 

So if you replace a 4.7uH inductor with 20uH inductor of the same physical size and construction the result will probably be lower maximum output current.