Does soaking chicken in water before cooking remove salt?

Yes it would help to remove salt. You may want to do this a couple of times with fresh water each time depending on how much salt you want to remove from the chicken.

The problem with soaking a raw whole chicken is that you spreading the exsisting bacteria from the cavity to all over the chicken. Modern advice from both US and UK health departments advise not to wash or soak a whole chicken before roasting. Some supermarkets use saline solutions to increase the weight of its cheaper lines of chicken breasts. At the end of the day you get what you pay for.