Let me expand on what Joe is saying by a bit.
OBT's aren't arboreal, terrestrial, or obligate burrowers--they are webbers. As long as you give them enough space, and make sure it is nice and dry, and has stuff to anchor webbing too they will be happy, because they can adapt. They do whatever they want to--if you give them an arboreal tank, then they're arboreal. If you give them a terrestrial tank, then they're terrestrial. So, yes, an arboreal setup is just fine.