Does the node count reflect the mining power support of different Bitcoin versions? In the current Bitcoin blocksize debate, xtnodes.com shows a pie chart of nodes running different implementations of Bitcoin; Classic, XT and Unlimited, etc.

Does this node count in any way reflect the mining power behind each Bitcoin version?
No, nodes and miners are separate entities performing different functions in the network.

The miners create the blockchain, which requires specialized hardware that performs hashing. The hardware is acquired through a significant investment.

Nodes are relay points in the network that verify, maintain and distribute the blockchain. They require (by comparison to mining) only a small hardware investment, or can even be run on virtual servers.

Nodes are much easier to be brought online, and can even be artificially inflated by responding to several IP addresses with the same node. Mining power can be directly measured by its output of proof-of-work. The numbers of nodes and mining power are in no direct correlation to each other.