You can be an American with Russian ancestry, and you can even apply and get US citizenship as a Russian citizen, but Russia doesn’t legally recognise US dual citizenships at all. In fact, they only recognise it with two countries, Turkmenistan and Tajikistan.
And if an American wanted to get a Russian citizenship, they would be required to renounce their American citizenship first - at least that was the case for a long time, I remember reading there being some work removing that requirement.
But you would still be seen only as Russian when in Russia.