Sorta, but it wasn't the hardcore doctrinaire sort of Marxism of a lot of punk bands (Gang of Four, Crass, etc.). It was more of the romantic revolutionary sort. Softheaded, maybe, but not evil. And they did rock.
As to his Marxism, I think that the movie Straight To Hell came about from some Marxist protest (concert?) that fell apart and so the gathered celebs and Alex Cox decided to make a movie quickly. Some of this backstory is in the documentary that is on the DVD.