Ben,
The logical fate diagram adorned the covers of the General Semantics Bulletin for many issues (years).
Fate applies to people and life.
Logical consequences applies to formulations.
Since Korzybsi wanted general semantics to be the application of "correct" scientific reasoning with empirical testing to ordinary life, he is asking us to apply logic in life. But the nature of valid inferencing is such that with true conditionals and true premises, the conclusions are guaranteed to be true. If our conditional theory of life is a true conditional, then our "fate" from acting will depend upon the starting premises.
"Fate" means approximately what will inevitably happen. Valid logic has the same "truth preserving" quality.
In other words, the fated consequences of acting parallel the conclusions of true conditionals with true premisses under valid logic.
Acting is like a premiss.
Cause-effect is like true conditionals.
Concequences (fated conditions) are like conclusions.
By analogy with math and logic, you cannot get to conclusion B2 from premis A1; you much change your premiss to A2 first.
The consequences of action is "fate" with no indication of the cause. But the consequences of action when logic is properly use is "logical" "fate".
So, yes, "logical fate" is part of general semantics. But it involves hybridizing the domain of mathematics and logic with the domain of cause-effect physical "laws".
In intensional logic, if we want a different conclusion, we must go back and change one or more premises.
In extensional behavior, if we want a different result, we must go back and change one or more starting conditions - in this case beliefs or "premises".
On page 207 of Manhood of Humanity, Korzybski quotes Keyser, crediting Keyser with the notion that "Mathematics is the study of Fate ... in the sense of the binding thread that connects thought with thought and conclusions with their premises."
Another part, facet, thread, etc., of general semantics that has it origin in the time-binding record of the preceeding philosophy.
Wait until you get to my age. Then you may have to look things up (like I do). 