Well according to the fallout wiki's Chicago page, and Enclave force landed there after the destruction of the oil rig. So that sets up the only BOS chapter to be known to have airships having a chance of getting vertibirds.
In reality there is no way of knowing for sure until we find out the date the game actually takes place in. In my prediction if it takes place within 5 years of fallout 3 there is almost no way it could be the CWBos unless by some magic they have managed to rebuild completely, secure the CW, and build an airship. Meanwhile the MWBos has had nearly a century of rebuilding so they could conceivable make the trip.
Both groups had access to Airships and Enclave tech, both had reasons to name there ship Prydwen. Also to the person who brought up taking one faction and transporting them across the country to make the game is that not how F3 got its major factions, they magically decided to move to Washington D.C. and we have what we have, there was tonnes of complaining at the time about transporting the BOS and Enclave to the East coast. Hints have been made for both factions in the writing of F3.
Personally I hope for the MWBos, the most organized and best path for the BOS to rebuild the wasteland (by any means necessary).