I tried to very carefully write the conclusion so that you technically don't have to have actually gone through the Gate for everything to make sense, though narratively that's the "best" way for it to play out. The very first paragraph after returning to the Galatia Academy changes. There is a holo of your ship going through a Gate, but it's kinda implicit to be a visualization of what the Janus Device can do rather than an actual recording of what happened.
So...
- In the case that you use the Gate, Baird says "We observed your $shipOrFleet come through the Gate."
- In the case that you don't, she says "We've been hearing the strangest rumors over hypercomm"
If the latter happened, then it's working correctly. Though maybe it's too subtle?