They haven't said that it's become permanent, but there also haven't been any rumblings that it's going away at any point in the near(ish) future. It doesn't seem as crazed now as when it first opened (and sold those red rose tumblers), but it still seems fairly busy. Given that BatB is a fairly popular movie (while it was converted when the live action movie came out, it's decor is a mixture of the live action and the animated movie - with more seeming to lean towards the animated movie), I think that it'll be the Red Rose Tavern for quite a while.
For your Pinocchio fix, there is still the attraction next door and Figaro up on the ledge in PFF (across from the store). Pinocchio and Jiminy are also in IaSW, and Pinocchio's Village is in Storybook Land Canal boats.