I would like to know whether its possible to look up to files and folders stored in box with the path of it like in dropbox. Retrieving id of the files or folders we want to access/manage seems like an overhead. Any help would be appreciated.
It is not possible to access Box files and folders by path. The file/folder ID is returned to you when the item is created and it does not change over time, so you might consider saving the ID if the file/folder will be frequently accessed.
Box is not unique in this regard. Here's a useful comparison of how several major storage services handle file/folder identification (among other things).