Yes they can but in the end the market will always re-balance and win.
Good examples right now are the Japanese and American currency policies.
Japan is dependent upon exports. For Japanese goods to be attractive to importors they must be as cheap as other goods of an equal quality. As America is a large purchaser of Japanese goods then the Yen must not get too far out of step with the Dollar. The Japanese have been regularily selling Yen and buying Dollars to keep the Yen from speeding away from the Dollar. They will chuck a couple of trillion Yen at the market and the effect will last about 12 hours.
America on the other hand has a weak Dollar policy. This is to support the export of American goods and keep Americans employed. As the majority of the worlds trade is conducted in US Dollars they can simply print as many as they want and spend them with other countries. This policy is starting to have a very serious effect in Europe where car and software producers are finding it increasingly difficult to sell into the States and could be delaying the return from recession in France and Germany. So, the American policy is certainly affecting the markets.
The bit that the US seems to have missed is that by advancing the state of the US economy at the expense of its primary trading partners it is in danger of biting the hand that feeds it. If Europe cannot sell into the States then there is a real possibility that by the time the US relaxes it policy that the damage to Europe will have been sufficient to delay Europes ability to trade with the US. In effect the US could make the best and cheapest widgets in the world but if the world cannot afford them (regardless of price) then America will not sell them and the market will find a painful balance and win again.
So, yes, a country can manipulate the markets but only to a point. In the end it will catch them up and bite them in the .....