We know Russia has done this successfully at least once.
According to Time magazine, a US State Department official estimated that the KGB may have spent $600 million on the peace offensive up to 1983, channeling funds through national Communist parties or the World Peace Council "to a host of new antiwar organizations that would, in many cases, reject the financial help if they knew the source."[13] Richard Felix Staar in his book Foreign Policies of the Soviet Union says that non-communist peace movements without overt ties to the USSR were "virtually controlled" by it. Lord Chalfont claimed that the Soviet Union was giving the European peace movement £100 million a year. The Federation of Conservative Students (FCS) alleged Soviet funding of CND.
http://en.wikipedia.org/wiki/Soviet_influence_on_the_peace_m...