Call me silly but I think about questions like this. It's a big state with only about 1.5 million people, even though it is the only place with six pointed star garnets (refined here). Much of the state is beautiful.
Imagine the counterfactual that, in 1846, when the U.S. and Great Britain resolved the border, one part of the area went its own way. Today an independent Idaho would probably a) be more "right wing" than the U.S. as a whole, and b) free ride upon U.S.-provided public goods, such as national defense. A federal Idaho government might be more concerned with boosting tax revenues (it would be full residual claimant) than is the current state-level government. All those factors would militate in favor of population increase. Most of all, I have the odd (Bayesian?) notion that since it would look and feel like an underpopulated country, more people would flow in.
On the other hand Idaho would face the risk of trade barriers and its legal order might be less secure than for the U.S. as a whole. The prospect of mobility barriers could either keep people in the area or out of it.
Does EU accession add or drain people from its smaller units, such as Slovakia and Estonia? There's much at stake here, yet governments sign on to many agreements without thinking about the long-term consequences for their populations, whether pro or con.
Note: The comments section on this post is not for rehashing standard debates over immigration.