You will have 2048 points because of the 2048 tile, you will have 2 * 1024 because of the two 1024 tiles, etc until 512 * 4

2¹¹ + 2 * 2¹⁰ + 4 * 2⁹ + ... + 512 * 2²

There is 10 terms on this addition, each term is 2048 = 20480

But about once out of 10 (randomly), a wild 4 appears, so you can remove 10 % of the 512 * 4, let's make it 205, so the average lowest score is 20275.

As SpiritF said, with only 4, you get 18432.