Sure you can do it. You can do anything!
That said, green
wood is notorious for binding nitrogen, so use as much green waste as you can and if you have access to mature manure use some of that as well and a thick dash of
compost to
boot. The Kultur isn't going to produce the same way as an old wood kultur would, but it is a great way to remove waste and not waste it...
I am working on a huge brush kultur as I reclaim about a tenth acre of
land that has been abandoned since Hurricane Sandy. It has entered primary succession but with mostly invasive species like multiflora, wineberry, bitter sweet and autumn olive. I have been cutting these, digging out the stumps, allowing them to dry and die and then layering with tons of oak leaves and a dash of compost and soil at each level. I am not cutting the green branches up small at all, but supplementing the possibility that they would bind nitrogen by adding plenty of it to the mix at all levels. Kitchen waste in the from of all veg scraps and spent
coffee grounds go on each level too and yes, plenty of
urine if you are up to it.
Just remember that ALL the tree needs to be completely covered. IF you have any old wood laying around, even in the form of small branches, throw those in right next to the green wood. Mature wood chips would also work well to introduce those cold loving wood fungus kiddies!
Good luck!