YES THEY DO!!!
Was in Melbourne recently for holiday and stopped by Hermes at Collins St. Bought a number of items in my wish list and wanted a few other items but they either didn't have my size or the color I wanted. In the end the nicest SA who attended to me asked if there was anything else I wanted. So I tried and asked whether they had any Birkin available. Honestly I didn't think they would offer me one as I was not a local customer. She said they did not have any at that moment but would checked with ther manager and asked me to wait.
Awhile later the manager came out and introduced herself as Susan (she was simply gorgeous

) She explained that Birkin are normally for local customer as there was a quota sent to each store meant for their customers. She asked whether she can refer me to the nearest store in my country. I explained to her the store in my country almost always have nothing for me plus it was 2.5 hours plane ride to get there from where I lived. That was why I normally buy my H items when I am on vacation. She thought about it for awhile and mentioned that they do have a Birkin 40 meant for a local customer who might give it a pass. But 40 was too big for me. Then she asked if I might be interested in an orange SBII ( could be due to the fact I was wearing a large watch with orange leather strap, orange and white clic Hs )
I couldn't say "YES, I'M INTERESTED!!!" quick enough

The SA came out a little later with the box and in it was the most beautiful and intense color I've evee seen- Capucine SBII