Is no-knead bread method compatible with stretch and fold during the bulk rise? Using the no-knead method (as decribed by Jim Lahey), instead of leaving the dough undisturbed during the initial fermentation period, would it be harmful to add in some stretch and folds to build dough strength? Would this be counterproductive, helpful or have no effect on the outcome? 

I'm thinking just randomly throughout the period, stretch and fold whenever fancy strikes. The idea is to make the dough stronger than it would otherwise be using the pure no-knead method.
Absolutely!  The Tartine recipe, the Ken Forkish recipe, the Jose Baker recipe and the America’s Test Kitchen recipe all do stretch and fold with their “no-knead” recipes to build the gluten structure. Definitely do it.