Hi Gray. I think if the biochar is for the forest garden where the soil is fungal dominated then adding to composted woodchips makes a lot of sense to me, along with some healthy forest duff/soil to inoculate the pile with the right fungi....or perhaps with something intentional like wine caps. I always add biochar to my woodchip mulches that usually also contain leaves. I have not seen any nitrogen shortage issues, but then I'm using it to top dress, not digging it into the soil so perhaps I wouldn't.
Adam regarding biochar being a carbon in composting....you're correct that the biochar is mainly carbon, about 90%, it's recalcitrant in form and really doesn't break down during composting (it takes 100s to 1000s of years to break down). There may be a little carbon present that will get eaten in the pile, but not very much. I don't count it as anything when I build
compost piles with it and the piles actually heat up more and compost faster than piles made without it.