As the absorption edge increases in case of degenearte n-type semicondctor because the Fermi level will enter in the conduction band and the electronic energy levels under the Fermilevel will be populated with electrons, similarly it will increase by heavy doping p-type as the Fermi level will enter in the valence band under the levels populated with holes.
So, yes the effect will be possible in heavily doped degenerate semicondcutor.
But we must be aware as the carrier concentration increases the energy gap itself between the conduction band gap and the valence band edge decreases, which is a phenomenon called band gap narrowing.
For more information please follow the link: Article Ahmed Shaker, and Abdelhalim Zekry, A new and simple Model f...
Burstein effect strongly affects on smaller energy gap semiconductors such as InSb from 0.2eV to about 1.2 for high carrier concentrati while it effect is small for large energy gap semiconductors such as CdS which affects by only abut 0.1eV or less for mor details please read the article published by
M. S. Omar and F. Y. Goges, 2006 Materials Science in Semiconductor Processing
The phenomenon of the band gap narrowing BNG is well known among the semiconductor engineers and scientists who works with heavily doped or strongly excited semiconductors where by measuring the BG as a function of the doping and or the concentration of the mobile carriers, it is found there is an appreciable band gap narrowing. This bandgap narrowing has a negative effect on the bipolar devices. Therefore it has been intensively studied in the literature to explain it and work out its origin.
I would like that you see the paper in the link in my first comment.