it doesn’t say if it uses one of their servers

It does not.

if the two devices should be up at the same time

You can’t sync 2 devices when they have no way to connect to each other, so no.

I would recommend getting a server. And by “server” I mean literally any computer with Syncthing installed and left on. Could even be an old phone or something (with sufficient storage). That way there’s always 1 device to sync to.