I did something very similar with an old strategy game called Age of empires II. Over the course of two years I went from a 1300 rating to 1850. I don't play chess, so it's hard for me to compare the scales, but I will say the highest players were rated around 2600. I think being 1850 put me around 90-95th percentile for active players-- there were less than 50 players over 2300, and only a few hundred over 2000.

My only real commentary is that trying to follow a progression like this can be profoundly, profoundly frustrating. You need to really make sure you're enjoying this hobby before you try to dedicate yourself to a trajectory like this. It can really make you feel like shit a lot of the time, as you find yourself continually repeating mistakes that other people breeze past without issue. It takes true love of the game and a great deal of patience and persistence to push through all the downspells.

Eventually I decided that I no longer wished to prioritize the game over other things. The enormous time investment was no longer a worthwhile trade-off for me, and I stopped playing almost all together. I haven't regretted it since. There's just so many things to do in life. I gave it thousands of hours of my time, and now the door is closed on that. Now I'm learning Ruby on rails!