I've never heard of it, and such a name in a official document will sound distinctly weird. If children with such names exist, I predict a lot of explaining for them to do in the future. They will have to explain all the time that these are their "full" names, not diminutives, when filling official forms.
I believe, that Russians who prefer Western ways would name their kids with Western or exotic names. not with diminutives of regular "Russian" names. Such trend existed even in the USSR - my school military instructor (who was an ex-military himself) was named Harry. Combined with his very traditional Russian patronymic it was rather funny (in a good way).