Yes, I have seen "cargo" trailers converted and used for camping and not just on ones own property.. I have seen them being used in campgrounds.
I see a couple of problems with the idea.
If you don't already have one laying around not being used, buying new or even used will cost you more upfront than a purpose built travel trailer..
Cargo trailers because of the nature of it's "universal loads" use often results in a substantially much heavier body and frame than is what is needed for camping use.. You will end up with a rig that weighs 25%-40% more than the same size camping trailer and that is with nothing inside the trailer. Purpose built camping trailers are designed to be camping trailers and not cargo haulers.
It will ALWAYS look like a "cargo trailer" no matter what camouflage method you try, which can be an issue in some campgrounds which are touchy about looks.
I at one time had looked at the idea of converting a cargo trailer until I saw the price tags of the trailers, windows, doors along with the weight factor.. Wasn't worth the hassle and cost to me..
I ended up finding a old used travel trailer in the length I was looking for for a mere $700, gave me frame and box with title, windows, doors, furnace, a/c, water heater, full tub with integrated surround, all three tanks and more other useful parts. I would do it again in a heartbeat but instead of removing and replacing the rotted wood framing and such I would cut the bolts and remove the top , sides and floor and start from scratch, much cheaper and quicker.
For custom designed and built camping trailers, you could check with some of your local trailer builders that build custom horse trailers with living quarters.. They may be willing to adjust their designs a bit to expand the living quarters to the full length of the trailer..
Custom built no matter what you try, will result in a heavier and much, much more expensive RV.. For price and weight, it IS hard to beat the standardized assembly line of RV manufacturers. So if you were looking to do this on the cheap, you will be sadly disappointed unless you plan to string hammocks from wall to wall and have no windows or any other creature comforts.