It helps for colourists to have neutral background colour because they need to be able to accurately judge the balance of what they are adjusting, but for home use as simply a viewer, I'd be surprised if it made much difference. I have some massive dark red curtains behind the set, for a start ... !
I can tell you that trying to balance photos with varying room lighting is a bit of a nightmare, you often wind up over brightening or pushing the white balance too far, but I've rarely noticed a difference in the viewing experience with different backlighting, unless it was too bright, which is a different type of failure..