Yes, but before that person had an even number of handshakes, so shaking their hand gets them to odd. But at the expense of putting him at even. At worst, it's a neutral move.
And like I said, it really depends on the other rules which are never explicitly stated.
But I have a sneaking suspicion that discussing the game is arguing the metaphor.
The game is just there to help us get to the realization that graphs with an even number of vertices can have an odd number of edges, but a graph with an odd number of vertices can't have an odd number of edges.
