There is a big impact in it. JK story also can be seen as TRUE continuation of the book and KOTOR+KOTOR 2
Also as a TOR player and a lore lover you HAVE to play Foundry Flashpoint (however Empire has a different outcome as Republic)
However (last however i promise =P) unlike WoW TOR has sort of a linear story and all of the character stories can be placed in a singular time line (You can youtube all of them to put the pieces of the puzzle together)
Sith warr and Sith Inq are unrelated to KOTOR ='( but they are still cool.
Hope this helps, feel free to ask more questions =D