It's a special-purpose design for constraint-satisfaction problems with simple rules, but complex interactions. E.g. when solving a Sudoku, the set of valid choices at every step is easy to determine, but you could make a series of valid choices that back you into a corner where no more progress is possible and you have to backtrack.
Meanwhile, LLM reasoning failures are more often of the kind where a choice is clearly invalid (as judged by a human observer), but the LLM picks it anyway, because the underlying rule is complex and context-dependent and the model only learned an imperfect approximation that often breaks down.
GRAM won't help with that.
But that's a very hard thing to implement, and the gains are uncertain. Thus "might".