I would say this is different for each person.
In my case I don't study theory and I am around the 1500s. I am also stable at this rating, so I am on the point where if I want to improve I need to do somethig else/more/different than what I am doing.
Still there is a lot of posibility to improve in other areas and still get to increase my rating whiout touching the theory, for instance, in my personal case improving visualization can do a great deal for me. So if I train in something like blindfold or other visualization training my score maybe will improve another 100.
What chess rating do you think can be achieved without studying theory? I don't mean the basics such as pins, etc. I'm talking about openings, endgames, etc. Sort of learning as you play.