Yes, they can climb when they want to. Seems like, if the head can reach a raised area he can pull himself up.
Also, while being watched my BP will be slow or motionless but I've seen him move unexpectedly fast along the parquet floor.
I don't want to confine him to the enclosure forever since he enjoys exploring, and will figure out a way to "snake proof" the living room so he can only wander in that area without getting into other rooms. Also now know to keep an eye on him whenever he's out and about!