I barely managed to reach 64 in the 3×3 board when it was game over. 4×4 is still doable, but 3×3 is pretty impossible to me.
That's mathematically not possible. Let's assume that you are very-very lucky and you only get number 4 tiles as the new ones.
That is 2^2, and we have 9 tiles, each of them twice as big as the previous one. That adds up to:
2^2, 2^3, 2^4, 2^5, 2^6, 2^7, 2^8, 2^9, 2^10
As you can see, 2^10 is the maximum possible we can have, which is just a 1024
So to answer your question: it's not possible to reach 2048 tile in a 3x3 version of the game(assuming that the rules are the same as with 4x4: 1 new tile after each move, which is either 2 or 4)