I imagine it all still goes through DDG, so it would be very difficult for Yandex to disambiguate more than a short stretch of a stream of search queries (let alone associate them with a person) even if they wanted to.

There's still the issue of individual queries revealing something that the user doesn't wish revealed. It would be interesting to see how exactly DDG uses these other search engines as sources (and if they are able to make demands with regard to logging), but it's worth noting that DDG logs search queries itself (just not associated with a person), so that may not be possible to ask for.