Yes you do, but apparently the Block perks do NOT apply to 2 handed weapons, which makes no sense. =/
Has this been confirmed? I was led to believe the right hand side of the block tree does apply to two handed blocking.
"Players can block with two-handed weapons and the perks Shield Wall, Quick Reflexes, Power Bash, Deadly Bash, and Disarming Bash all apply to two-handed weapon combat" on Skyrim Wiki.