A general knowledge of the prequels and original trilogy would let you get more out of the series, but it isn't 100% necessary.
And as >>108942952
said regarding past material; Any past EU material was often adapted or reworked to the story/setting (sometimes to fan dismay). Essentially identifiable for fans to pick-up the references, but not to the point it should be a detriment in drawing new fans (like pic related, EU fans will know who these Clones are, but it isn't necessary for non-fans to know where from).
It also would be good to keep in mind that the Disney acquisition of Star Wars occurred as TCW was in the middle of airing so if you do want to look things up on a wiki, there's quite a bit of Legends material on this series.