No, but if Korinth isn't being bottled up by Athens, it is going to contest our slowly growing hold on the Adriatic, and it may even do so immediately-- "beeline" towards that goal, to use your terminology. That is a fight we currently cannot win. If the situation in the Adriatic devolves into war, we have a good chance of losing political control of Nea Kymai. In fact, we've even seen the blueprint for how such a conflict might erupt with Kerkyra!
To be honest, I'm getting real Kerkyra deja vu off your vote. You're voting to send the oligarchs-- who have existing tensions with the rest of Kymai, to Nea Kymai. Simultaneously you're voting to put a culture & prestige generation machine (the oracle) in Nea Kymai, making it an even more tempting target. Furthermore, you know that we don't have the current naval capacity to fend off Korinth and our agreement with Taras prevents us from throwing our lot in with Athens.
So the realistic course of events (if Korinth makes a play for the Adriatic) is that they will rouse the oligarchs against the people of Nea Kymai, overthrowing the government. Then the Oracle will become a Korinthian possession in fact if not in name. And unlike the Athenians, we don't have the navy to koolaid man our way through Korinth's navy and then kill off the oligarchs. It will be a shitshow.
Oh, I don't know, one of these has a wall? And a navy nearby? And isn't in the Adriatic?