Dropping oil prices will deal long-term damage to the Russian economy. Given the current state Russia is in with Vladimir Putin using money to send his troops into the Ukraine, falling oil prices will devastate the economy as there will be a huge loss of profit for Russia. This loss of profit will contribute to long-term damage to the Russian economy as combined military costs and lost of revenue will have a damaging effect.
While the Ruble took a very steep nosedive over the past few days because of new lower oil prices I don't think they are going to stay there long enough to negatively impact Russia for the very long term. It will be a rough couple of months and then it will get better.
One of the main reasons that US sanctions against Russia have had a limited effect are because Russia continues to profit from its large natural gas reserves. Many European countries buy their natural gas from Russia. But with cheaper oil, oil becomes a more viable option for meeting energy needs, and Russian profits may suffer as a result.
No, the oil price drop will not damage the Russian economy in the long term. Although lower prices may be damaging to their economy in the short term, prices will eventually go back up and their economy will recover. This cycle of lower prices will just be a short term issue for their economy.