Probably not. Compression only works on files that have lots of redundancy. For example, source code files (C, Python, etc) have lots of redundancy because some symbols are more common than others. Executable files have less redundancy and cannot be compressed as well. To be effective, bitcoin dat files should have low redundancy. Encryption techniques also reduce redundancy in files because redundancy provides clues to an attacker.

The real solution might be to find some way to collapse the older transactions into some sort of archive so we newbes don't have to down load more than a couple of years to be productive. If the archives were distributed over the internet they would be available everywhere as needed.