No. His friends and associates would be saddened but not shocked. Almost everybody in the population would have had no idea that Shakespeare had died, and many of them would never have heard of him any way.
William Shakespeare died in 1616.
William Shakespeare died on 23rd April 1616.
william shakespeare died at the age of 52.
William Shakespeare Burton died in 1916.
William Shakespeare Hays died in 1907.
William Shakespeare - cricketer - died in 1976.
William Shakespeare died in 1613.
William Shakespeare - singer - died on 2010-10-05.
William Shakespeare Hall died on 1895-02-11.
I gather you are not talking about William Shakespeare the playwright who died in 1616. You should probably specify which William Shakespeare you are talking about if you are not talking about the obvious one.
William Shakespeare died on 23rd April 1616.
William Shakespeare does not have a future. He died in 1616. That pretty much ended his career.