No. While
Leonin Arbiter is in effect, it's not possible for you to search your library, and when a resolving spell or ability asks you to make a choice, you cannot choose an option that's illegal or impossible. (CR 608.2d)
When
Ghost Quarter's ability resolves, it gives you a choice: {search your library} or {do nothing}. That first option is impossible thanks to the Arbiter, so therefore, your only legal option is to do nothing.