When I started this thread, I was particularly thinking of a song called "The Pump Chanty" on the CD Keep Calm and Seek Revenge by the Pyrates Royale. It contains a segment which goes (from memory, so I may not have it exactly):

The Captain says It's Roll and Go
But I think we're bound for Davy Jones

What I didn't realize when I started the thread, but which I now suspect, is that this may be a contemporary song, written "in the style" of a shanty. If so, it doesn't of itself establish "Roll and Go" as a traditional nautical term. But I have the impression (supported by some of the responses to this thread) that I have heard the expression in many songs or other usages, always associated with the sea.

Don