Discourse peut-il prendre en charge un forum partagé pour deux sites web avec des styles distincts ?

So, if a user opens site A, goes to the forum from site A, then theme A is applied.

Then the same user opens site B, goes to the forum from site B, and sees theme B?

What if the user has the theme A applied, goes to site B, and refreshes the forum page? Does it apply theme B, or does it keep the theme A?