I don't veggie-garden, but I do garden. I can tell you that the no-till mulch-heavy gardens will take a couple of years to really get going if you simply apply layers of mulch. Last year, I put together a new ornamental garden (based upon mostly antique roses as the "bones") from scratch, and the soil here in my new home is awful -- imagine bricks, smashed. The band-sized roses were potted with a mix of equal parts peat moss, shredded hardwood mulch, and Bovung dehydrated manure, with organic granular fertilizer mixed in. Cardboard was laid down where the beds would be, and then topped with a few inches of snipped branches and green leaves from a Callery pear I was hacking back to bring sun in to the yard. When the grass and weeds underneath were dead, the roses went in the ground (late Summer). In mid-Autumn, I had 15 yards of composted shredded mulch delivered, and put it down to about eight inches thick. By Spring, it had settled a couple inches lower. Before I planted perennials, I worked composted manure into the mulch.
Lessons learned? If I had to do it again, I'd have put down a layer of organic fertilizer on the tree trimmings before adding the mulch to speed up decomposition. I'd also have used a layer of "Mel's Mix" from Square Foot Gardening over the top of the mulch before planting -- the mulch did a great job of keeping things moist down below, but it severely diminished my germination success with direct-sown annual and perennial seeds. "Mel's Mix" is equal parts peat moss, vermiculite, and compost. The vermiculite is good because it's inorganic (i.e. it won't break down) but helps retain moisture. It's a bit expensive to use on its own, however, so mixing it with the peat moss and compost helps to stretch it for the garden. And being inorganic, once you have the amount you want in the bed, it doesn't need replenishing -- you add only the organic stuff as it breaks down.
Throwing down one thick layer of mulch was what I did because it wasn't practical for me to do things in multiple repeated layers, but it's really better that way. And I'll be adding alternate layers of nutrient-rich fertilizer and manure with nutrient-poor peat moss, vermiculite and mulch as I continue to move along. You want layers because it encourages the earthworms to move throughout the bed. If you have to do things the way I did (thicker but fewer layers), put the largest-particle-size on the bottom, working your way to the finest stuff on top. Rain and earthworms will do the mixing for you.
Wood mulch is not all the same -- the bark nuggets take the longest to break down, whereas the shredded stuff may be half-gone by the end of the season (if you get lots of rain). If you want the mulch to break down faster, you'll need to add organic fertilizer that's high in nitrogen. This could be used chicken litter thrown on top, or organic lawn fertilizers. The wood will sop up nitrogen as it decomposes, but will then re-release it gradually into the soil. If you are veggie gardening, don't remove the tops of the plants at the end of the season -- just snip them into bits with a set of pruning clippers, throw down some organic fertilizer, and smother with mulch or tree leaves for the Winter. For my garden, I do the same with the top-growth on herbaceous perennials and annuals at the end of the season.
Pest problems? Not really an issue for me where I live, and what I grow, so I can't really comment there. But I can tell you one thing -- while pests seem to be able to thrive in disturbed and chemically-altered environments (e.g. conventional gardening, even with pesticides and herbicides), their predators are more picky. So when I decided to go organic, the first year the pests were out of control. But then the predators came, and as long as I keep their needs in mind, the damage is minimal. For example, the first year, rose slugs were an epidemic. This year, the wasps and mantids and birds have discovered good hunting grounds in my yard, and I haven't seen as many rose slugs as last year.
Long story short -- going no-till and using the layered mulch approach does work, but not immediately. It takes time for everything you throw on the bed to decompose and get incorporated into the existing soil. But once it gets going, and your first layers have fully composted, it's great.
