Especially if there is a lot in the culture about Tashbaan/the horns at the gates etc as representative of the greatness of the people.
For sure Cor and Aravis are really well placed to become very very skilled and useful ambassadors/operatives. As for Rabadash (and everyone) finding out the story - I expect it took about a week (or less!) for the Archenland bards to turn the whole story into a lay for recital/song at feasts (it is told by a poet in The Silver Chair.) Which isn't diplomatically very savvy, but then, people aren't, often.