No, it has nothing to do with the "Golden Dome" nonsense.
The US did all sorts of war game scenarios and plan making during and directly after WWII and they've never stopped.
There's actually probably a lot of countries who have done the same, though I'm not sure to the extent the US has.
The fact that the US has a plan like this by itself isn't newsworthy. Who it's coming from makes it noteworthy because, while the plan may have been created decades ago, it's a very unsubtle threat against another nation.
I agree that this is stupid, but understanding is important because this is how they weasel out of things. If confronted or challenged they'll say, "Oh, that plan was put together decades ago." Everything they do is done with cover because not only are they fascists, they're cowards too.
Short answer, yes they can.
Long answer, it's really going to depend on the state and the laws there.
That said, common etiquette would be not to unless, as someone else pointed out, they had a very specific reason to suspect an illegal immigrant is in the vehicle. Usually, LEOs stick to their specific jurisdiction's unless they are asked to assist in another.
Typical federal agencies would notify and work with law enforcement, but sanctuary states have directed state and local law enforcement not to.
They are breaking the law and violating a US citizens constitutional rights, that's where America is right now.