Yes, most everything that you mentioned will grow well in unfinished compost. I do that all the time, due to a variety of reasons.

First, I like that I can get huge amounts of wood chips (the most acid of all organic amendments) for free, from tree companies. When they arrive, you have to put them somewhere, or your wife will divorce you, and that is on top of the beds. The chips are easy to move around with a pitchfork, whereas finished compost is much more of a pain (I produce small amount of finished compost for seedlings only).

And the chips (or grass clippings, or leaves) do eliminate weeding, the chips for two years or so. Clippings and leaves, likewise, are easily movable with a pitchfork when they are still whole. Clippings go under plants as soon as they are produced, while leaves overwinter away from the garden only because piles of leaves turn into mice cities around here in the winter, otherwise they would go on the beds right away.

Then you are left with the problem of having temporarily acid soil. For fruit trees and berries, that is not a problem. You will just mulch them with chips indefinitely, and they will be happy like that. I can guarantee that blueberries, raspberries, hardy kiwis, grapes, blackberries, pears, apples and currant are quite comfortable with wood chips only. All my flowerbeds and perennials get wood chips only, except irises and moonflowers, which need wood ash.

The pH of the soil will rise as the matter decomposes, to the point where eventually the soil will get close to its original pH.

There is a particular sequence that one has to follow to take advantage of this varying pH. Basically, amongst common veggies, potatoes will grow in wood chips that have been only slightly amended and are still too acid for most everything. In that soil, still not totally finished, the next year you will be able to grow tomatoes and squash and melons. The next year you can grow chicory (radicchio) and garlic. The next year you can try pole beans and collard. The next year the soil should be well done.

Other large amounts of wood chips go well as a thick mulch (on top of finished soil) for tomatoes, all cucurbita, pole beans, collards, garlic and onions, and herbs. At the end of the season, I rake it in one pile at one end of the bed, and that will be a potato patch next year (repeat rotation).

That is basically how I manage my soil. About 60% of my 8 beds were once wood chips. I use kitchen compost, which is quite N-rich, to correct the nitrogen deficiency of the chips. I also use urea and manure from my neighbor's horses, to the same effect (essentially N management).
You have to add some N to unfinished compost, depending on its original green-brown ratio. You may have to add N for a few years.

I use a lot of leaves, which produce nice, somewhat unfinished compost by May which is friendly to most vegetables. I particularly like leaves compost with lettuce.

Finally, for some veggies even years later the soil remains a bit too acid. I add wood ash, which I have in great abundance. Virtually all veggies benefit from wood ash in my acid soil, but greens (arugula, rapini, bok choi, kale, tatsoi, spinach) and beets, in particular, can not grow without some. They prefer a more alkaline soil. I use wood ash basically for pH management.

So most everything will grow well in the soil you have, if something looks poor, look up its optimal pH, then put lime or ash under it, on a case by case basis.