In "The Devil and Tom Walker" what possible plot developments does the mention of buried pirate treasure invite?

This sort of interpretation depends strongly upon the individual reader, as well as their understanding and literary connection to the concepts of treasure, pirates and hidden things. For example, we might expect that an American reader has a concept of pirates that more or less follows the tropes depicted in media such as "Pirates of the Caribbean", whereas a person more familiar with Somali pirates, or internet pirates, might have an entirely different series of connotations. 

Buried or lost treasure is often used as a narrative device to spur characters into action. In film, it might be called a MacGuffin - something which drives the plot but is, in and of itself, relatively inconsequential. Consider, for example, that the treasure would have zero effect on the world if no one knew about it. 

The most straightforward plot development we might assume the treasure invites is that it will be discovered, and allow its new owner to achieve some sort of ambition. It also fulfills an aspect of the stereotypical American ideal of rising to the upper class through one's own efforts, or some sort of ingenious trickery. Similar themes are drawn upon in "The Great Gatsby", and ultimately the money itself is not as relevant as the character traits and transformations that it brings about.