Yes, it's possible using steady state absorption spectrum. Do you have the absorption spectrum of alumina ? Then just using the cut-off wavelength from the spectrum in the formula E=hc/lambda calculate the band gap energy. Hope this answer helps you. By cut-off wavelength I mean where the absorbance value is minimum before showing a distinct rise. You can infer the same cut-off wavelength information from the reflectance spectrum also.
I have not done Uv Vis yet i am just doing literature survey on Al2O3 but i did not get any paper which shows the relation to calculate band gap from uv data for al2O2 as is shown by tauc relation for other semiconductors like ZnO and other also