Will the WoL be branded as exiles for lore?
By the game itself - probably not. As Enla mentioned: Playing an Au Ra has no real effect on your mainstory either, even if it (logically, specially judging by the build up of Yugiri) should have.
Within Eorzea and most likely the better parts of the Far East, being a Viera in exil doesnt really matter either - why should a pirate in Limsa care about the reason a Viera is running around in his city? No one in Eorzea would have any reason to "brand" you as being someone in exil. You're just another adventurer and how you came to be one, matters fairly little.

Will there be other lore integrated into the game to explain what happend?
Happend... how? Do you mean lore in regards to why the players character left the Woods and became a Viera in exil?
Most likely not. No other race got that sort of treatment either (again, mainly pointing at the Au Ra) - and I doubt they gonna change that now.
The WoL is a blank canvas by design, so if you want to play a Viera, you can make up your own reason how you ended up as a puglist in Ul'dah - did you sneak onto a merchant-ship in Kugane to leave the Far East behind? Where you maybe caputerd and sold as... exotic dancer to some rich dude? Did you hide your ears for months and tried to pass as Hyur only to leave eventually? Did you hear Hydaleans call and ventured out of the Woods, not caring how people reacted towards you? - instead of having a backstory provided for you.
Keep in mind: For the purpose of the story your Viera will be the only one who ventured out of the Woods, except for any NPCs, obviously. Even if you fight Nidhogg with 6 other bunny-girls, your bunny-girl is the outliner, the only one who ever left the Woods. That doesnt require any new "lore", because its not lore, its the backstory of one character - your character, so you have total control over that.

Can the NPCs dressed like bunnies in the Gold Saucer be switched to Viera?
...why would they be? They're clearly based on playboy-bunnies, given the enviroment they're in - and not on Viera. The bunny-outfit isnt some placeholder for Viera - its a "sexy" bunny-outfit, based on ...clothes that actual hostesses would wear.


If not is it now culturally appropriate?
I dont really understand this question? Do you mean that it might not be appropriate anymore to have those girls in bunny-outfits once we have Viera as a race?
In that case I would like to raise two questions of my own:
(1) How culutrally appropriate is it to put women into those skimpy clothes in the first place?
(2) Have you SEEN the Viera race-gear? Have you seen Fran? The bunny-outfit is tame compared to that... so is your question wether or not its culutrally appropriate for a bunny-look-alike-girl to work as hostess in the Gold Saucer?