Would a chiropractor be able to tell if I have a back or neck disease just by feeling my back and neck?

Probably not. Chiropractors operate under the notion that all backs are abnormal. The inciting event is your visit - proof that something is wrong. And they will always find something by a combination of touching and blasting you with unshielded, high energy x-rays to find non-existent pathology. If you suspect a problem, see your family doc or orthopod first.