GoPro Recording Without A Phone Connection
Yes, it is entirely possible to use, operate and record on a GoPro. 

You won't be able to view any of the photos/video you have taken without either connecting to a mobile device OR viewing the footage you have taken on the MicroSD with another device such as a PC or Mac.

The GoPro cameras have a fairly wide angle lens which is helpful considering the cameras don't have a display built-in. GoPro sell removable LCD touch screens that can help you to frame your shot.