To be able to culture the yeast, it has to be unpasteurized, unfiltered. You should be able to see a bit of yeast in the bottom of the bottle. As far as I know, Sierra Nevada leaves all their beers unpasteurized, not sure about unfiltered, but they used to be unfiltered. So you might be able to do it.
However, in this case, I'd say why bother? All SN beers use the same yeast and it is probably the single most popular homebrew yeast ou there. You can buy it as Wyeast 1056, White Labs WLP-oo1, or Safale US-05 dry yeast. The dry yeast is so inexpensive that it doesn't seem worth the effort. You'll spend more money on extract to step up the starters than you would on US-05.
Currently On Draft: Bamberger Rauch Dunkel, Belgian Blond, Pilsener Urquell clone, Smoked Porter
Bottled: Concord Pyment, Mi'Apa Sparkling Mead, Chimay Blue, Old Simcoe American Barleywine, Old Cantankerous
Fermenting and Conditioning: Pseudo-Decoction Munich Dunkel, Left Hook Bitter
Recently Kicked Kegs: Fresh Hop Pale Ale, Citra Rye IPA
On Deck: Old Rasputin, Northstar IPA, Ur-bock Dunkel