With some adjustments, yes.
The General Strength workouts are just that, so they don’t need to be changed.
However, muscular endurance workouts should be made specific for the event being trained for. The linked article explains the difference.
Also, timing. We usually prescribe Runner ME as a base period series of workouts and Climber ME as a specific period series. (Specific period meaning just prior to the goal event.)
With general aerobic volume, the volumes and relative changes could be the same, but the benefit will be greater if the mode of workout is specific to the goal event. So run* when training for a running event. Hike uphill when training for a climbing event.
* Note that “mountain running” is an oxymoron for most. Most people hike the ups and trot the downs. That’s what mountain run training should look like as well.