Can generalized twenty questions be solved by a greedy algorithm?
No. There's a huge literature on the topic, called combinatorial search theory, you can read more about these types of questions there.
The simplest example that I could think of is the following.

Suppose that you want to find an edge of a graph, and you can ask whether a given vertex is incident to the hidden edge, or not.
Now take the following bipartite graph.
It contains a perfect matching on $100+100$ vertices.
Moreover, it also contains $10$ degree $10$ vertices that are connected to $10$ different vertices each, all on the same side.
So one side of the graph has $100$ vertices, all degree $2$, the other $110$, of which $100$ have degree $1$, the other $10$ degree $10$.

In this case, the greedy algorithm would first query the degree $10$ vertices, and then the rest, taking about $110$ steps.
If instead it started with querying the $100$ vertices of degree $2$, it would be done in $101$ steps.