Hello Dawn, welcome to permies :)
The shrubs themselves, along with the top soil beneath them (which turns into a sort of "peat-moss" from leaf and seed debris decaying over years), are full of nitrogen which might be a nice
boost to help you develop your eden garden a bit faster.
As TJ says, even when not chipped Caragana wood will decay quickly, so you may need to compensate that with another type of wood chips. Then again, if your
yard is similar to the ones around here, you may have an endless supply to restock with. I' rent 2 lots in a small village and have about 400ft of caragana. I think I've cut them twice in the last 7 years, so it takes them about 3-4 years to grow back to full height again. Even when everything else dies from winterkill, they just keep coming back,
I like to think of caragana as the poor man's bamboo of the prairies - or at least a different kind of fast-growing shrub with other valuable uses. It also makes good
kindling as it catches fire quickly and you don't have to chop it up with an axe because it's already the right width.
Have fun! :)