For the most part of the USSR existence, no. All the government officials were members of the communist party, and you couldn’t be religious and a communist at the same time. Even on ordinary people’s level religion was discouraged. It wasn’t forbidden, but it was extremely hard to have a career if you are openly religious (even you just wanted to baptize your kid, so your grandmother would stop to worry).

This slightly changed after 1985 (perestroika and glasnost), and there was some guilt about the soviet church policies, and there was some need in spiritual guidance because all older ideals seemed to be lost. At first, Christianity perceived as a part of the Russian culture, but slowly it became something more. I’m not sure that soviet officials began to show their religious side at that time, but, anyway, if someone did it it should have happened after 1988-1989.

But in 1988-1989 new faces began to rise. And it became a new tradition for Russian (not the Soviet, USSR was dissolved in 1991) officials to show their respect to religious institutes, including their participation in some religious rituals (all-night Easter service, for example).

Christmas Day became a national vacation day in 1990 (in Russia). Orthodox Church was officially registered as an organization in 1991 (I’m not sure about its status before that, but anyway it was a big deal). A lot of restrictions were removed. A lot of properties were returned and rebuilt if needed. New laws allowed to teach religion in universities. And so on.

It’s hard to say was Yeltsin the true believer or not, but during his presidency he did a lot to make the Orthodox Church richer and stronger (as well as some other traditional religions in Russia: Islam and Judaism, but to less degree). He participated in public religious services from time to time, and a lot of other government officials also began to attend. But it was Russian Federation, not the Soviet Union at the time (although many of these officials were communists and soviet officials just ten years before that).