Lets assume one thing:
1. Everybody has the same mediocre talent in chess.
With that assumption out of the way, I can safely say that without proper study and study materials, everybody will level out sooner or later.
This comes down to your person, YOU. If you are content where you are, then you won't improve, or have little chance thereof, even with study as your heart just won't be in it. Now if you wish to improve and truly WANT it, the number of games and study will help you improve, if done correctly.
I was very recently rated about 1200 and had been sitting at that rating for a couple years. At that time I was thinking the same thing you are now, "Can I improve?". It certainly didn't feel like I could. It felt, in fact, that I was playing at the top of my game! Then I began studying. A month or so later and here I am at 1400.
Short Answer: You will improve, if you put the work into it. Know, however, that it takes talent to break a certain level. But sheer hard work and determination should take you up to a title, perhaps as high as IM. That, however, could take years and years to achieve.
I think three years ago when I first started playing chess, my rating on chess.com, or my strength was something like 1200-1300. now my rating, or strength is 1550-1620.
Am I going to continue to improve or am I going to be like this for the rest of my life?
For people who have been playing ten years or more. Do ratings continue to climb or do they level out at a point. I believe that 1600 is too low a level to be a plateau and I feel that I still have much chess in me that has not come out.