Are you sure about that? It doesn't completely rely on it but didn't it use bing as one of the search providers? I'm probably completely wrong and my info is outdated but I'm asking because it would be pretty special (in a good way!) if they use their own index exclusively.
Qwant was not usable yesterday during the Bing outage so that pretty much shows they cannot function without Bing (even if they do have some auxiliary indexes of some sort)