Nope... This effect will increase its frequency, but not its speed. As it
approaches a BH, it gains energy, given by E = hv (where h is Planck's
constant and v is the frequency). Since its speed is a constant given by c
= wavelength*frequency, its wavelength will also decrease as it increases
in frequency. So light will "blueshift" towards shorter wavelengths, but
won't increase in speed.
-YEAH BABY I CAN'T IMAGINE THAT YOU'D WANT ME TOO-