I like creative thinking! I'm just not sure why we would want to turn our gaze in the direction of some idea that is not much in evidence and then research and speculate to that end.

The song was in books of spirituals by the 1880s.

First published sailor-related mention I have in my notes is 1903, in a review of one of Basil Lubbock's books. The reviewer notes that Lubbock mentioned several chanties but neglected "We'll roll the old chariot along."

The song turns up in the collecting work, amongst sailors, of Gordon and Carpenter in the 1920s. Of the lyrics available to me, there is no mention of such a narrative of going ashore. One of Carpenter's men had "If the devil's in the way we will roll it over him."
And Doerflinger (1951), from Dick Maitland, got, "If the devil's in the road we'll roll it over him." Both spiritual lyrics.

The "grub" lyrics come in Wood's 1927 _Oxford Song Book_. Author got it from a Mr. Walter Raby, who presumably was the one who told him it was "a windlass shanty popular about forty years ago [i.e. 1880s] in Lancashire vessels." Verses are extemporized. Wood's chosen verses (from Raby?) mention scouse, sea-pie, plum duff, and a glass of whiskey hot. [Note that Doerflinger reprinted these lyrics.]

That's basically where my notes on it end. I hesitate to delve into some of the other post 1920s "collections"! I know Hugill has it, but I don't have it handy. I'd be wary, in any case, of what sort of "slant" he might have constructed in the way he presented it. He certainly had read Doerflinger, and might have wanted to play up the "old salt" stuff (as he was wont to do). I'll check later, if no one else does, first.

In all, I don't see much reason to follow a "rowing" or "going ashore" theme (the "night with a whore" sounds suspiciously like a "in bed with the captain's daughter" thing -- what's the source?).