In Stan Hugill's Shanties from the Seven Seas, he says:

"[Shallow Brown] started life as a pumping song. It is I feel of West Indian origin, some singers giving the refrain of 'Challo Brown' -- 'Challo' being a West Indian word of Carib extraction meaning a 'half-caste', and heard as far afield as the ports of Chile."

Hugill lists four versions of Shallow Brown, not counting other songs featuring that name. He goes on to say,

"At some time or other this Negro song pased through the shanty mart and was used by the cotton hoosiers of Mobile as a cotton-screwing chant. Sometimes the wording would be that of Sally Brown, and 'Oh, Sally Brown' would be substituted for 'Oh, Shallow Brown' in the refrains."

He also mentions a fragment called Shiloh Brown, which is "a version of what appears at first glance to be Shallow Brown but which in actual fact is a variant of Tom's Gone to Hilo."

There may be more information in the "related threads" link at the top of the page, but I was too lazy to check them.

So, I guess the songs are referring to a generic character rather than a historical person. But I'm sure that if you created a biography of Shallow Brown and started passing it around shanty sings, it would soon become the received truth!

Aloha,
Mark