Yes. There are no restrictions (copyright, music..etc) related to posting the output of your template based GoPro Studio generated videos.
It is possible that YouTube will display a message stating "Your video may include music that is owned by a third party" if you are using the Shotgun Barrels template with the Small Town Zeros song "Secrets". Here is an image showing the message:
If that happens, just click “Acknowledge” to accept the fact that monetization on that video production goes to the Artist.
There should not be any issues with posting videos to Facebook.