In this day and age when vast amounts of knowledge can be obtained at the speed of light, is it possible to produce a writer with a minimal amount of education like Mark Twain or Walt Whitman?

It is, but it may be difficult. Yes, there is an unlimited amount of resources available, literally, at anyone's fingertips if they let their fingers do the walking over their computer keyboard. However, a great writer is not just one with a great deal of knowledge.

A great writer is someone who can envelope a reader into their world through the written word by writing about experiences they have actually lived through and that is something that cannot be done sitting in front of a computer.

For example, Mark Twain wrote books based on childhood experiences (The Adventures of Tom Sawyer/1876) and Walt Whitman wrote about his own life experiences (Leaves of Grass/1855).