I haven't got the references to hand but Gibb has several contemporary references to SB being used as a rowing song in the first 2 decades of the 19thc and it appears to be an embryonic form of the chanty. It certainly seems to be one of our earliest chanties. 3 others are 'Cheerly Men', 'Grog Time o' day, and 'Going down to Georgia'.

There is some evidence to suggest that 'Cheerly Men' was an English work song used on small Naval vessels well before the American developments.

I back Reinhard's statement. There may or may not be some vague connection in the use of the name SB.