Yes, it is possible to have Sins installed on 2 PCs and play through LAN with one registration It's explicitly allowed in the EULA, as well.

If Stardock ever dies in the future, they've said they will untie any serial key authenticatioins from the games, and you can always install from the archives.

Each game has their own EULA, however for all Stardock-published games (GalCiv 2, Political Machine, soon-to-be-Demigod) this is typically allowed. There's nothing technically built into Impulse or the games that would not allow you to do this, but if Impulse is providing a download from another publisher, it may be against that EULA, since Stardock has no say in those.