Assuming Mozilla isn't compelled by law to share it's entire database of user information on a rolling basis without a warrant, I suspect (in the U.S.) it would be somewhat effective at shielding yourself from bulk metadata collection (government mass surveillance) of your online communications by obfuscating that metadata.
Compare this to your ISP and telecom providers. A subset of the larger providers willingly handed over the communication metadata of their users without warrant.
Compare this to your ISP and telecom providers. A subset of the larger providers willingly handed over the communication metadata of their users without warrant.