To what extent can cryptocurrencies be influenced by monetary policy?

Well first if actually the cryptocurrency we are talking about would be created by central bank, then the rules that were used to create it would be by definition monetary policy even if supply of money would be fixed, since monetary policy is central bank’s control of money supply either directly or via interest rate (see Yeyati, Sturzenegger (2010), or Friedman 2001). Keeping supply of currency completely fixed at all times is a valid (although arguably very disastrous) monetary policy. Hence, to an extent that some monetary authority consciously sets up rules for cryptocurrency, that set of rules will, by definition, be monetary policy.

If we are talking about some independent cryptocurrency then the cryptocurrency is equivalent to being a foreign currency from a perspective of central bank. In such case we can’t talk about central bank directly conducting monetary policy for cryptocurrency as by the definition of monetary policy monetary authority has to be able to change supply of money, but despite of that monetary policy set for its own currency can still affect the exchange rate between domestic and cryptocurrency and thus it can affect the value of cryptocurrency. A loose monetary policy ceteris paribus, would depreciate USD/Bitcoin exchange rate making bitcoins more expensive (for more detailed overview of how monetary policy affects exchange rate markets see Exchange Rates and International Finance).

Central bank could decide to do what you suggested buying/selling that cryptocurrency - which is equivalent to an foreign exchange intervention. This too is technically monetary policy since this is done through control of the money supply of central banks’s currency (e.g. central bank has to create more of its currency in order to get more of the foreign currency as reserves, and conversely when it reduces the foreign currency reserves it will get the previously created money back and thus reducing money supply). Even if a central bank has no control directly over money supply of other countries this allows central banks to also to certain degree control value of other currencies. For example, in past China’s central bank was partially keeping dollar overvalued and yuan undervalued by keeping large USD reserves.