What are the space requirements for a tall Jungle Tree trunk?

Can I dig a deep 2x2 shaft in the ground, plant 4 saplings on the bottom, give them light and bonemeal and have the tree grow to the very surface? Or does the space requirement mean there must be free room around the trunk?

I read there's no upper limit on the height of Jungle trees. Can I force the tree to grow very, very tall that way, by digging deep enough?