I don't think so. It's not really more efficient than long division, with the same number of operations for each digit of the big number. Most of the improvement for humans comes from the fact that you get to deal with smaller numbers (0-9) for a section of those operations than with the bigger range 0-19, but the computer generally doesn't find it easier to multiply by one 64-bit number than another.

In any case, integer division and modulus are implemented at the hardware level. I think tricks like this could improve the modulus operation if the processor vendors wanted to add additional dedicated instruction codes for say, divide19. For most workloads this will not be a useful thing to do. But you can't rule it out: before Bitcoin existed nobody built processors which were optimized for calculating millions of SHA-256 hashes in parallel.