Yes, the data should fit in the c4 register. c4 is limited to a depth of <= 512. Read more here:
https://ton.org/docs/learn/tvm-instructions/tvm-overview

If you use cells in a linear single ref tree, you are limited to 512 * 1023 = 523776 bits or near 64 KB. But if you use all cells to store data, it's a very huge tree with a lot of space. Only at the bottom layer it has 4 ** 511 cells.