Hmm. Russia's major exports are oil and natural gas. Oil and natural gas are priced and paid for in dollars. If Russia drops the dollar, it just means they'll trade the dollars they get for some other currency, which has no net effect upon international currency prices. Or perhaps they'll request that nations buying their natural resources pay in something other than dollars; oh well, then that nation will have to exchange dollars for a different currency, again affecting nothing.
Russian can't affect the total supply of dollars in circulation, which is what primarily determines the prices of dollars. Only the US government can do that. China could hurt the US somewhat by refusing to buy any more debt (what people usually mean when they say a country is dropping another currency), but Russia doesn't buy enough US debt to make a big dent if they stop doing so. This is an empty threat, if it's even a real threat at all.