This sequence, where Pinocchio escapes from Pleasure Island and discovers that Geppetto has gone searching for him, is very much exposition. It marks the end of the second act and the start of the third.
The letter from the Blue Fairy is somewhat clumsy. Why doesn't she appear herself? I'm guessing it's because we need to see Pinocchio make the decision to go after Geppetto on his own and not have him come to it through discussion. Still, to have Jiminy reading the letter in order for the characters and the audience to learn information is pretty poor storytelling.
One of the interesting things about animation here is that Woolie Reitherman is one of the few animators who gets to do more than one character in a shot. During the early shots with Pinocchio running, Reitherman handles both Pinocchio and Jiminy. Later in the film, there are shots by Reitherman that include Jiminy and Monstro.
Reitherman's Jiminy is solid in this sequence. There's good comic animation in shot 12 where Jiminy is trying to dry off and in shot 29 there's a terrific take when Jiminy realizes that Geppetto has been swallowed by a whale.
While this sequence is built around Pinocchio's moral turning point - his independent decision to do right by rescuing his father - the direction and animation throw this moment away. There is no shot of Pinocchio wavering between fear of Monstro and the love of his father. Such a shot would literally show his thoughts and coming to a decision. I think that the film missed a major personality opportunity by not including this. Certainly Frank Thomas, the animator who did Pinocchio in these scenes, was capable of pulling it off. However, the film wastes Thomas in this sequence. What's here isn't particularly taxing from an acting standpoint and lesser animators could have done the job equally well.