I don't know about using copper tubing. I would be concerned about copper leaching into the water column. While it's not as important to fish, if you plan on having any inverts in this tank, the copper could be deadly. There are much safer and easier to work with materials.
Remember, drinking water safe and aquarium safe are 2 different things.
and cement on a diy tree could get quite top heavy. Also with the weight on the branches , if they flex, the grout will crack. Maybe foam/drylok would be a more safer way to go?
Just a few suggestions