It's a good question. Theoretically, it would be possible, and there is already a non-public script I made that can loop through the entire dir structure and create IMAGE cache and JSON cache (for folders and menu). However, Files app currently relies on making requests to PHP, which checks if cache exists, and then returns the cache (if cache for the request does not exist, it will have to be created first by PHP, and then returned).
I will check tomorrow if this is possible in current release. Else, I'm sure it could be made possible.