I remember having owned a recording of Pete Seeger singing "Go Down Old Hannah (Don't You Rise No More)" during which he speaks a bit about how "Hannah" means the sun. Sorry I can't recall which album ~ maybe one of those "Best of Newport" anthology LPs.

Calling the sun Hannah probaly predates calling the wind Maria, so I'd say that the Broadway-show-tune reference was "in the tradition of" the slave-era work song, not vice-versa.