Of course not.
Mozilla can install extensions if you have "shield studies" enabled. They use extensions it to run UI studies and things like that. I think you have to opt-in to each study individually if you want to be part of it. Enabling the studies in your settings only means "notify me when there's a new study I can participate in".
See https://support.mozilla.org/en-US/kb/shield and https://wiki.mozilla.org/Firefox/Shield/Shield_Studies
Now they have partnered with Mr Robot to use the same feature to offer some sort of "Alternate Reality Game".