Very possibly. Interestingly, Wyoming is a possible *goal state* choice, a state that sends two senators to congress, but only one representative. Even I can remember that my congressman represents the First Congressional District when there's only one.... I'll even put him on my Christmas card list. [Well, actually *her*: Republican Barbara Cubin holds the seat at present, and I don't think she has too much to worry about from a challenger, though when she steps down, her replacement may face a challenge.]
And don't expect the locals in a thinly-populated area to greet 20,000 outsiders with hosannas and hymns of thanksgiving.
Some will view them somewhere between a plague of locusts and an outbreak of political rabies, I'm sure. But there will likely also be a few businessmen and merchants who might see 20,000- or more- new customers as their potential salvation.
-archy-/-
If the economy can absorb 20,000 new customers in a relatively short period of time--which is something I strenuously doubt. Like I said, there's good free market reasons for low-population states to have low populations.