No. You are actually more likely to contaminate your kitchen surfaces that way by splashing water all over. You can go either way on chicken though and that's because you may have a little feather or bone debris you might want to get rid of. Any bacterial contamination will be destroyed by the heat of cooking. Bacteria won't penetrate muscle but ground meat should be thoroughly cooked.
Yes , you are always supposed to wash raw meat before cooking it ! Always . Raw meat carries a lot of germs and bacteria such as E Coli . That is an extremely dangerous and fatal bacteria ! Wash meat and be safe .