It can be done and it can work but you need to remember that the trees will continue to grow and change shape. We had a big birch growing through part of our cabin when I was growing up. It required cutting out a little of the floor and roof every couple of years to keep the tree alive and so it did not grow around the wood. If you design it to allow for this you could leave them there.
The other option is to keep them. Build the shelter using the trees as your corner supports. Then girdle the trees. This will kill them but keep them standing in place. You now have you foundation and supports. The trees are dead though and branches will eventually start breaking off.
It is difficult to free fools from the chains they revere - Voltaire. tiny ad:
A rocket mass heater is the most sustainable way to heat a conventional home