Yes & No.
There are separate pools for Canadian, NZ, and Aust. Kittyhawk IA, III & IV. And for things like Hudsons, Venturas, B24s, and Spitfires. Canadia has its own Hurricane pool, too. Patrol aircraft as well.
BUT: The "Commonwealth" nationality aircraft pools are available, generally to all of them. Those pools contain mostly carrier capable types, and the Tiger force bombers. (Lancasters, & Lincolns. But not the Lancaster B.1 Spcl - that is RAF only, along with the Mosquito B.35.)
And to complicate things more, the RAAF and RNZAF eventually get their own pools of P51Ds, but they have a normal range on DTs 380nm less than their USAAF counterparts.
There are exceptions that reflect historical anachronisms. There are, off the cuff, and not an exhaustive list:
- A USAAF squadron (group?) that can commandeer some 'spare' Dutch B25Cs in Australia.
- HMS Victorious arrives with USN TBF-1s in its strike group*, which has something to do with its alter ego as USS Robin.
- an RAF wing (broken down into two "5" series squadrons) that turns up in Aust and uses RAAF Spitfires.
- a USAAF Cargo group than can borrow C46As from the Chinese pool.
* I think that if you swap them out, you can't get them back.
"You may find that having is not so nearly pleasing a thing as wanting. It is not logical, but it is often true."
- Cdr Spock