Kimchi juice to aid lactic fermentation of half-sour pickles
Short answer is "yes".

Sour pickles don't get sour because of yeast. Pickles get sour due to lactic acid produced by bacteria, the same way kimchi works. Propably you could even add a bit of real home-made yoghurt to boost the bacteria. The bacteria needed are already present on the cucumbers (even after you wash them, but you shouldn't srcub them too much!), and addition of bread heel, kimchi juice or youghurt will just boost their growth.

As a seasoned Polish sour-pickles maker, I can assure you that you don't need the bread or kimchi juice at all. The pickles will get nicely sour without it, but they will just take a few days more. In summer I prepare sour pickles with the bread, in order to have them ready really fast and always on hand, but for my winter jars I never use the bread. If I put the heel in a jar that's supposed to wait till winter, the cucumbers will overferment, might get soft and generally will be good only for cucumber soup.

My other comments on the receipe: using iodised salt is fine, as long as you don't exceed half of all salt used (the other half must be pickling/kosher salt). It is not just the brine that keeps them from spoiling - it's mostly the lactic acid. The "pickled water" is sour enough to prevent fungi growth, and it is extremely rich in vitamin C and is a great cure for hangover ;)