As with so much else in security, it depends on your threat model.
"Can someone in another country (assuming that you are not right at the border to that other country, and the adversary is immediately on the other side of the border) use the network pre-shared secret (the password) to gain access to the network?"
Generally, no. The frequencies used for wireless networking have very limited range (mainly because of atmospheric attenuation of the signal, plus attenuation in things like walls), and even if someone uses a high-powered transmitter, they still need to receive the signal sent out by your access point, the transmit power of which they supposedly cannot control.
But if the adversary is determined (and powerful) enough, there is little stopping them from parking a car, perhaps equipped with a directional antenna, within range of your network. (You can get pretty good range with physically even moderately sized directional antennas at 2.4 GHz, let alone 5 GHz, and that gain works on both transmit and receive.) At that point, if they have the password, they will be able to connect to the network and participate on it from a much greater distance than you'd be able to with just a wireless-equipped laptop or similar.
Now, the next question becomes: is that a likely scenario? I would say not very. If your threat model included that, you probably wouldn't be asking on a public web site about mitigative steps.
So, in theory, yes, it could potentially be a problem. In practice, as long as you do not reuse the network password anywhere else, you should be fine. That includes the administrative login to your access point, or router, which is good password hygiene anyway (never reuse passwords). If you currently are reusing the network password somewhere else, I would suggest changing both. And if you reused the password somewhere else, it's mainly the sharing a password that you are using for something other than what you consciously decided to share the password for that is the problem, not the network access.