Sure there were writers who led normal lives--at least relatively normal. William Carlos Williams was one of the great poets of the early 20th century. He was a physician who lived in a fairly small neighborhood and who bragged about the babies he had delivered. Wallace Stevens was another of the great 20th C. poets. He was an executive in an insurance company in Hartford where few of his colleagues realized he wrote poetry. T.S. Eliot led a relatively normal life. Many of the first American Nobel winners (in literature) were alcoholics, but even that is fairly normal.
I believe there are writers still living who lead normal lives. Richard Russo and Jonathan Irving and Joyce Carol Oates come to mind, but I certainly don't know enough about them to be sure.