No. Better to compost the vegies in a compost pile, then use the decomposed compost.
If you must use fresher material then yes, chop it, but then spread it around the whole area and till it into the soil, do not leave it in any sort of pile, and absolutely do not create a pit under a new plant with chopped material.
I doubt that it would actually hurt the plants...this link has a reference to a Youtube video in the comments that shows exactly that. I think after a certain amount of time, it would be the same as composted material...
Mother nature puts these materials on the surface, where oxygen is a primary factor in decomposition. I would recommend putting this material near plants, but not under. You may want to investigate sheet composting.
Oh, yes, after a while it is compost.
The problem I see is that when you first put the chopped material in a blob under the plant, then add the soil the plant is sitting higher. Then it decomposes (pretty fast in the summer) and the plant sinks. Then the surrounding soil falls against the stem of the plant. There are not many plants that can handle getting more soil added to cover part of their stem.
Also, a dense blob of chopped vegetables may attract flies or any of several other pests. If the same material is blended with the soil there is no such problem.
Lets deal with the chopped vegies like this:
Dig a hole for the plant. No deeper than it is now in its container, but 2-3 times as wide.
Blend the chopped material with about half to 2/3 the soil you just dug out. Not more than 50% chopped matter. As small as 30% is fine.
Put the plant in the hole and backfill with the chopped matter/soil blend.
Lightly scatter more chopped matter around the plant.
Use the remaining soil to build a berm around the plant, on top of the chopped material. The berm is to hold water. The additional chopped material under the berm will rot in a short time, supplying the growing plants with a slow trickle of fertilizer.
Water well, filling the berm a few times right after planting, then use the berm to help water for a few weeks while the plant is young. Eventually the roots will spread into the surrounding soil, out beyond the berm, and you can rake it down.