Sounds good, may want to stack them two high to accomodate deeper roots. Also be aware that all that surface area exposed to air and no bottom will make more frequent watering necessary to prevent drying out the roots.
You may try the same thing with pole beans or peas or cucumbers on your balcony. Just put up a piece of re-mesh or 6"x6" field fence as a trellis. The large openings in the fence let you reach through to pick produce without going around (off the balcony?). Even squash can be grown vertically this way, if they get too big make hammocks for them using old pantyhose or other scraps of lightweight mesh material. Just tie the ends of the hammocks to the fence wire for each veggie.