SAT-solving expert here. No immediate applications (the results in the paper are "galactic"). The main question is whether some ideas here will snowball into other ideas, one of which could eventually be very practical.
** Yes, I know that's proven to be impossible.
If objects have a maximum size of 4 GB (= 2^35 bits), then arbitrary objects can be sorted in O(n) using 2^2^35 bits of memory.
Yes, I think we can pretty safely say that the algorithm in the paper is not used due to practical constraints. This is a subjective judgment, but pretty clear from the paper that the algorithms aren't practical to apply.