Before introducing complicated workarounds, I’d ask Yandex first.
A single boolean flag with “don’t exchange pictures/ignore server-supplied picture” semantics hardly qualifies as a “complicated workaround”. (Basically, “don’t use PHOTO field”.)
As for asking Yandex… I have. And all I got from them so far is a pair of links: one to their official CardDAV/CalDAV setup page, another - to 4pda.ru forum. Not exactly useful.
On the subject of complicated workarounds… A complicated workaround would be to store the encoded picture in the NOTE field of the contact card (with some additional markup, of course) and send it to Yandex that way. I tried and it appears that Yandex servers accept it, store it and then serve it back in its unspoiled form. So, that would actually work around Yandex refusal to store PHOTO… until they get wise to it, probably 🙂