Every BoxCryptor Folder contains a configuration/key file. By default this is named ".encfs6.xml" but as Box Sync does not like files beginning with a dot very much, the name of this file is "Keyfile.bcx" when the BoxCryptor Folder is located within the Box Folder. So yes, also when using other services such a file (with a different name) exists and is sent to the cloud.
But as David pointed out, the important parts of this file are encrypted with your password - so anybody with physical access to this file still needs to know your password.
We also have some information in our Knowledge Base: