If any activity is set to private within Strava, it will not be synced with a Wild Challenge leaderboard. If you wish to have the activity included in any leaderboards, you will need to amend the privacy setting to either 'Followers Only' or 'Public'.
You can still maintain effectively private on Strava by setting your Strava account and activities to "Followers Only" and then only allowing followers you approve. If you want no one to see them, you can choose to have no followers. Your activities will still sync into your Wild Things account and count towards challenges and FKTs.
In the interest of openness and fairness, purposefully hiding activities during a challenge period until the end, or purposefully splitting the same activity into multiple (by stop-starting your watch for example) is not permitted as this is not in the spirit of what a challenge represents, and prevents all other members from being able to compete openly.
Purposefully hiding or splitting activities until the end may result in those points not being included.