Does Saturation velocity in semiconductors have a relation with the wavelength in which the peak in the absorption spectrum occurs? 
Saturation velocity is the maximum velocity a charge carrier in a semiconductor, generally an electron, attains in the presence of very high electric fields. 

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I want to know if the absorption peak can be calculated with this parameter when a semiconductor like GaAs is under illumination.
 A: Well you seem to be mixing apples with oranges.
Absorption of a photon in GaAs  depends on the bandgap of the material (taking doping into effect) and the photon energy, and doesn't have much of anything to do with electric fields.
The effective collection of any carriers generated from the photon absorption may be influenced by the electric fields, but that is usually not an important effect.
GaAs used as a PV solar energy collector, is invariably operated in the forward Voltage mode, so there aren't any very high electric fields; and if you use it in reverse bias mode as a linear detector, then you don't want to use very high Voltages, which will increase the leakage.   If you use it in avalanche mode, then you can get a signal gain, at the cost of noise and linearity.  But my digression doesn't really answer your specific question which relates to the peak of the absorption spectrum.    Processes which create long wave tails that are normally absent, may change the spectrum, but that would have little effect on the wavelength of peak absorption which is not a tail "fringe" effect.
