When the New Tab Page errors, it typically redirects to the local New Tab Page.  However, the interceptor does not catch bad certs:
chrome/browser/ui/search/new_tab_page_interceptor_service.cc

Neither does the throttle it is soon to be replaced with:
chrome/browser/ui/search/new_tab_page_navigation_throttle.cc

Perhaps cert errors to be sent to NavigationThrottle::WillFailRequest, but at this point, they don't.