Yes antibacterial soap does help with body odor.
When you have body odor the body odor is usually caused by bacteria that harbors on your skin and when you wash your body off with antibacterial soap the antibacterial soap kills the bacteria that causes the body odor.
So when the body odor bacteria is killed the body odor should go away.
Antibacterial soap washes away other bacteria and germs as well as viruses that may be on your body.
So it's a good idea to wash your body in the shower using antibacterial soap.
Washing your hands often as well using antibacterial soap also helps get rid of bacteria and germs and viruses so wash your hands very often as well.