I think you can know nothing about a statement even if you know what it is, so you can update on finding out that C is a conjunction.

Did you mean "can't"? Because "can" is my position (as illustrated in the dialogue!).

Given that we aren't often asked to evaluate the truth of statements without knowing what they are, I think my sense is more useful.

This exemplifies the point in my original comment:

Of course, we almost never reach this level of ignorance in practice, which makes this the type of abstract academic point that people all-too-characteristically have trouble with. The step of calculating the complexity of a hypothesis seems "automatic", so much so that it's easy to forget that there is a step there.