Ok... sorry, I thought they were on the same local network.
You could always just connect on-demand. When I need to connect to my dad's network, I enable WG on my computer (the endpoint at his house is an OpenWrt router).
If the IP address on the 'server' side changes, it would disrupt the wireguard tunnel. This may happen both quickly and infrequently enough that it isn't noticable at human scales. But it would require re-establishing the connection. I think a change on the 'client' side would not likely cause this problem.