You sometimes hear about hugel beds that have gone without irrigation, even in dry climates. I have not had to water as much since developing my wood for food garden beds, but up until this summer I had never cut irrigation off completely.
This year I decided to try stopping irrigation in a few places to see how the plants would fare with only the moisture from the rotting wood. Once in a great while I sprinkled a little water from a jug (a few times over the whole season), but these plants were not really watered. And -- we went for about 80 days with no rain this summer!
This zucchini plant is in the center of the non-irrigated bed, with aspen logs and manure underground. It has beautiful zucchinis on it now and looks more robust than some of the other zucchini plants I have growing in an irrigated, non-hugel bed.
The potato plant next to the zucchini is doing just fine too. On the other side of the zucchini, I dug a hole yesterday and found the dry soil to be full of potatoes, with no plant in sight. It appears that the plant formed its potatoes and then died, perhaps due to lack of moisture. However, I harvested the most beautiful red potatoes I've ever grown -- beautiful skins, no blemishes, perfect flesh. Works for me!
This zinnia may have picked up some moisture from a neighboring micro-sprinkler, but the Swiss chard and celeriac in the background were not irrigated at all. (The zinnia is coming into the picture from an acute angle -- its base is a few feet away.) Both the chard and the celeriac volunteered in the straw-mulched path, and I just let them go. The path receives no irrigation, but they didn't seem to mind at all. They are growing in a mixed-species hugel bed.
Based on these experiments, it seems that you really can grow food without irrigating, once you have a moist sponge of wood available to your vegetables.
Happy fall gardening!