If you did that you'd see a odern-day Jew. He might be "Ashkenazi" or he might be "Sepphardic"; we also don't really know how much genetic drift has taken place amongst the Jewish population over 2000 years of diaspora and pogroms. So you may or may not get a very good idea at all of what Jesus looked like from looking at a modern-day Jew.
That actually has been researched. Assimilation is a very recent phenomenon: about two hundred years long. Genetics is largely there.