No - the GPS tagging of metadata is a single value and you should be able to discern if it's the start / end or (very unlikely an average) by empirical testing and an app like ExifTool or just the map for photos.
You will need to have a second app to log GPS coordinates separate from the video.
This is quite easy now as there are many motorcycle and other cycling and car racing track apps that capture detailed time evolving GPS tracks in known formats and also video recording - some with overlays.
DIY solution would be to start a workout on Apple Watch and Video on iPhone and know that both are time synced quite accurately for something like a 10 minute or longer video.
The newest Apple Watch Ultra has a significantly better GPS hardware / software stack than the current watches, so you might choose that if you have poor coverage or need meter resolution. The older watches are really quite good and with software path smoothing (see RunMeter / CycleMeter apps) they are excellent for vehicle paths in my experience and you don't need the fancy receivers for almost anything but precise spot measurements or forest / low coverage areas such as urban or wilderness canyons.
All of this could work on the same iPhone as video recording doesn't interrupt the workout apps in my experience.
Your only question is in what data format do you analyze / combine / synthesize the data into one presentation or digital file. I think you'll need a Mac or Windows app to transcribe the watch / workout coordinates into overlay characters and then mix it into the video if you're looking for something custom and not an existing racing app that overlays GPS onto the recording of your performance.