soap literally dissolves oil, that includes the oil on your skin
the purpose of the oil on your skin is to repel water, not water on the outside, but it keeps the water inside your skin by repelling it inwards. If you remove that oil, with soap, then your skin quickly starts loosing water through evaporation and it dries out. If you've ever washed dishes by hands you'll feel your hands dry out after because dish soap is kinda harsh on oil because it needs to be to do it's job.
Different types of soap have different qualities depending on the type of oil that was used to produce it. (yes, soap removes oil but it's also made from oil) Some like de-greaser are super effective on oil and grease. Others soaps are less oil absorbent/dissonant. All the body wash with moisturizers does is use a less harsh form of soap, along with a few added chemicals to reduce the drying effects of having no oil on your skin.
tl;dr yes
