If you have a coach or a strong player helping you, it means you are already studying chess. The op asked if it is possible to improve, without studying.
It is possible to improve without studying, but the improvement will be somewhat limited or it takes more time to rise to a certain level. What I think is a fine solution for Corbellino is mostly play and have fun, but when getting curious, he can study what he wants.

Btw, Nakamura played bullet almost every waking moment when he was a teenager. He got pretty good.
Nakamura as a kid has his step father(a master) to help his chess development.
@OP You can still improve without studying, but it will take much longer for you to improve and you might hit a road block on your improvement that you might not overcome. An improvement ,that you might find after many years playing, a 1 hour of chess study might give you. Solving few puzzles per day won't take much time and will improve you.
If you can identify that roadblock, then you can work specific on that roadblock, maybe with a course, maybe with a strong friend or chess teacher. Maybe with analyzing alone or with computer. Or even better, the best way to analyze is after a otb -longchess tournamentgame with a strong opponent or a strong player in your club. Blow that roadblock to pieces, and move on.
If you have a coach or a strong player helping you, it means you are already studying chess. The op asked if it is possible to improve, without studying.