I have dry skin and can vouch for the fact that your body tends to "find a balance" if you stop using soap, and I would imagine that it would be similar for those with oily skin (it could be that you are creating a lot of oil because the soap is drying out your skin.
On the other hand, you may find that you just end up even oilier.
The only way to truly find out would be to test it yourself. You may just want to try a less drying soap so your body doesn't need to generate as much oil.
Single data point: I had oily skin in my teens and early 20s, stopped using shampoo and limited my soap use in my mid 20s, and have had people who use many products to maintain their excellent skin remark on how nice mine is. Haven't tried going back onto facial soap to test how much of that is due to aging.
I don't know if this is true, but i have a theory.
Shampoo removes natural oils from the hair. The scalp responds by increasing it's production so you get oilier hair. It could be that the same happens with shampoo.
