Yes; this can be done by editing the blueprint or the specific child event itself. Follow these steps:
  1. Click Edit next to the event
  2. Select step 3, Select Event Options
  3. Scroll down to Related Actions and select Edit Advanced Options
  4. Select part b, Define Event Options
  5. Number 18, Participant Search Parameters, gives you the option to allow people to search for participants registered for all TeamRaiser events, for the specific TeamRaiser event only, or for the current TeamRaiser event and other TeamRaiser events of the same type
  6. Click Save