Yes it is possible.
These are the steps I just took to verify.
- User-A creates a folder called 'shared folder'
- User-A makes that folder publicly writeable
- User-A passes the shared URL to User-B. The key part of the URL is the id=1bxxxxxxx
- User-B goes to https://developers.google.com/drive/v2/reference/files/insert#try-it
- ... where he authenticates himself
- ... creates a request body containing parent: "id_from_step_3"
- ... Executes the upload
The result is that User-B has created a file in the folder 'shared folder'