Way back in the olden days I would not use wood chippings and sawdust horse bedding even though it had horse droppings and urine mixed in with it. Eventually I tried it but dug it deep into the top soil. It rotted down and made a good friable compost. So I started to use it like farmyard manure and straw horse manure in the top spit.
I never ever used shreddings or chippings - until one time I wanted to raise the allotment a little. I used chippings deep in the subsoil. This had the desired effect of raising the top soil up but no other noticeable effect. So I started using it a little less deep to help the drainage of the veg. beds. I did not dig it into the top soil still thinking it led to nitrogen immobilisation.
Last year I decided to use chippings, shreddings and sawdust mixed as a thick mulch of about 5 cm all over the allotment. I'm not sure whether it had much effect on yeilds but it certainly stopped the weeds. It had nearly completely rotted down by the end of the season and the last of it was dug in.
During the winter I have been experimenting with composting this woody material in the dalek bins and remarkably it is decomposing into some interesting friable material that looks like peat free commercial compost. I am composting it with ordinary kitchen and allotment waste and watering on comfrey liquid and "recycled beer" if it looks dry. I would suggest that keeping compost damp is one of the main rules. I turn this compost every two days and have already put copious amounts of this rich, well decomposed compost back on the allotment and spread it over the surface. Using this very woody material for composting has surprised me no end.