This question provides an interesting thought experiment. The rub comes with the "analogously" part of "...analogously to the way immiscible liquids do."
You could ask, for example, are dogs analogous to jellyfish...but the answer would be "yes and no."
Gases do "settle out" on planetary scales. Helium can (and will) escape the earth's atmosphere. So if you made a bottle big enough to hold the earth inside, the helium would be the "top layer."
However, when we think of the miscibility of liquids, we are often thinking about the interactions between molecules that force congregation or separation (polar non-polar interactions, for example) and not gravity related thermodynamic-style considerations. If you compress a gas out of a mixture of gases, then you made a liquid, or tricked a gas into separating using Graham's law.
If we mean, miscibility as the property of substances to mix in all proportions. Then yes, we can mix gases in a bottle at standard state. Dalton's law would hold.
If we mean miscibility as a strict homogeneity only seen under conditions of rest then nothing is absolutely miscible, really.
But...I love your question and it got me researching some fun articles.
Check out atmospheric concentration and vertical structure, it is fascinating!
It might also interest you to look up some articles on mixture settling. http://webserver.dmt.upm.es/~isidoro/bk3/c07/Mixture%20settling.pdf
Hope this is useful to you!