Looks to me that to me that looking things would be fast thanks to BBP, but it doesn’t look like there is a simple way to compress the data, meaning a way to discover at which Pi’s digit your file starts.
I see 2 problems:
How do you find that your 256kB of data in particular are actually at the Nth position? I suspect that they will be veeeeery far in Pi’s digit, so very long to compute the “compressed” data
If I’m right, I suspect the index in Pi will be so large for any large file, that it could be larger than the file itself. My intuition is that someone even already proved that.