Your new friends seem to have a rather odd interest in our cause, odd enough to make me question the legitimacy of their good intents, but I'd say the idea is at least worth the risk. While an alliance with the Core will not present any changes in our lives in space - as the Core operates in entirely different parts of Sirius than our ships do - the listed things will definitely change our lives outside space.
Gadgets, weapons, technology? They're offering us -this- in return for cardamine, drinks and shigeakiki? Sounds way too good to be true, especially considering that they can probably acquire cardamine from the Outcasts that they admittedly are in "neutral terms" with. This whole deal sounds like a "too good to be true" situation and whoever disagrees with me on that is encouraged to speak up.
I've nothing against the Core, but this whole thing sounds very unrealistic. I wonder what Matriarch Kiri thinks of this.