App Export Compliance using the Dropbox API
If your app uses SSL (HTTPS), then yes it does include encryption. The export compliance rules changed last year though, so you will need an Encryption Registration Number instead of a CCATS number. See this blog post for details.
As it happens I'm working on this right now on a related project.
The Apple position is clarified in the FAQ in iTunesConnect; (my bold)
If your App contains, uses or accesses standard cryptography for purposes other than those listed in questions 2-4, you need to submit for an ERN authorization. Examples of standard encryption are: AES, SSL, https.
This authorization requires that you submit an annual report to two U.S. Government agencies with information about your App every January.
It's a pain in the neck, but that is the law if you want to be fully compliant. I'd love to hear that I'm wrong though!
PS. You could always ask for a direct opinion from the Government department concerned here;
You can also call the Bureau of Industry and Security help desk at 202-482-0707 or read the web site at http://www.bis.doc.gov/encryption for more information.
Discussing your question with a live person is probably going to be better than filling out the online form and waiting for a response.