I'm reading Stephen Whitfield's "A Death in the Delta, The story of Emmett Till" right now and Whitfield states over and over again that the white southerners felt that the NAACP was funded by the Russians to help break down American society, he however does not state whether this was the case or not. I find it hard to believe that its true, but if it is, it sounds like it could be an interesting story. Whether it be small donations here and there or whatever.
I'm not aware of any such ties.
In fact, Thurgood Marshall, when he was the head of the NAACP Legal Defense Fund, was notoriously heavy-handed in removing people who would be viewed as communist. Marshall informed the FBI on alleged communist efforts to infiltrate the civil rights.
Sources: Thurgood Marshall: American Revolutionary by Juan Williams.