No, the third party doctrine allows for compelled disclosure (through warrants) of a user's data which the service acted as a carrier for. That's why law enforcement can send warrants to Google (or your ISP) to get the contents of your email account, rather than having to serve you a warrant.

The part that is often cited as being "voluntary" is that you decided to volunteer your information to a third-party (even if the service requires you to do so, and thus you actually had no meaningful choice in the matter) and thus you have "no reasonable expectation of privacy".