By default Boxcryptor only handles the encryption of the files and leaves the synchronization to the software provided by your cloud provider. It only works with your local copies and is limited by the available space on the local drive.
You can however try using the portable client: https://www.boxcryptor.com/de/download/?platform=portable
This version is intended for cases where you have to access your encrypted files without synchronizing or installing Boxcryptor.
It runs without installation, connects to the cloud and can simply be deleted once you are done.