Is just signing a piece of paper for a debt legally binding?

Most attorneys like to be paid, or, at least, the chance of being paid. If your boyfriend has no asset or job, most attorneys likely would not take the former wife's case unless she is paying money up front.

The note that he signed may not be enforceable, depending on what information is on the note and how they went about getting the note prepared and signed.

An attorney would need to know a lot more about the situation to give informed advice. What your boyfriend should do is review his specific facts with an attorney.