Nothing bad will really happen to you if you do not wash your back when showering or bathing.
But there could still be sweat on your back as well as other bacteria that could lead to acne on your back in some people.
I use a back scrubbing brush to reach my back when I take a shower and I feel so much better after I started washing my back.
I use body wash on the back scrubbing brush and it cleans my back really good.
I did used to break out with some acne on my back and also sometimes had itching on my back but after I started washing my back every shower I take I no longer have an itchy back or that acne that used to appear.