Is it possible to sync a folder from Dropbox to iBook in iPad?
No, this is not possible since iBooks does not support bulk importing of content from other applications on an iOS device. The three ways to add books to iBooks are:


Purchase from the iBooks store and download
Sync books through iTunes
Send a single book (not several) from another application on the iOS device with the Open In...iBooks option


Also, iBooks does not have the concept of folders and folder hierarchies. It does have Collections, but there is no way to map folders to Collections from iTunes or any other source.