Yes, if you focus correctly and have enough time you could become 2.000 (Please note the sentence "enough time", this is necessary until they discover how to adquire knowledge using pills like in the Matrix where they just insert information directly to your brain a moment before you get killed by agent Smith). So, let me answer for you the following questions:
Is a 2.000 player way stronger than a 1.600? Yes, in terms of probability, a 2.000 player has 91% chances of winning vs a 1.600. (If you want to calculate more of those odds go to
http://www.3dkingdoms.com/chess/elo.htm)
Elo rating has a mathematical calculation and meaning in real life; this is, if you know the Elo of two players you could estimate their winning odds. Even though, you wouldn't know the final result for every game because that depends on many other circumstances including your opponent quitting the competition because his girlfriend got pregnant and he has to get a job and start doing something profitable.
So, what would a 2.000 mean in terms of players, lichess and winning chances? Well, it means you have a higher probability to win against other people than a 1.600 player does. Right now being a 2000 in this site means to be better than 90% of the players. Righ now I see about 20.000 players in the site, so you would need to be better than 16.000 of them approximately. (This is: They shouldn't be able to beat the crap out of you so easily)
How can I defeat all those people? In chess almost everything is about not making mistakes, whoever makes them has to pay, and managing your time is also important. So, if you make two perfect moves but it took an hour for you to make them you will lose the game (Assuming you are playing with time control).
If you want to defeat them you will need some tools. If you work on the following list you will improve and if you focus enough you can get to 2.000 according to your learning speed:
1. Chess. What is this about? Is it worth it or should I better get a life? (I'm serious about this last part of getting a life, chess can consume a lot of your life)
2. How can I think better in general terms and what should I learn to start improving in chess? (At this point you will need at least one book, choose whatever you like but choose something more than just playing others, playing is fun but you're not necessarily learning from your mistakes, and learning is mandatory if you want to improve. Sometimes learning means to review your games and understand a little bit more of what is going on and why you are having such a hard time winning vs a 10 year old little russian girl)
Warning: Books needed also for the following subjects:
3. Opening. What is this about? What is good what is bad?
4. Middle game. What is this about? What is good what is bad?
5. Ending. What is this about? What is good what is bad?
If you don't improve after researching and trying to improve, just keep trying and researching even more, don't you like winning? Then stop whining and learn how to beat more players.
You're welcome!