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?

Solution 1:

Coming right from the wiki: http://www.minecraftwiki.net/wiki/Tree#Jungle_trees

For growth to succeed, there may be no blocks adjacent (even diagonally) to the north-western sapling (which is considered the center of the tree) up to the final height of the tree, as well as no blocks 1 block away except at the same level of the sapling (even diagonally).

So in order to successfully grow the tree, you would want to dig a 4x4 hole. Also:

Large jungle trees can grow up to 32 blocks high.

There is an upper limit.