This is basically just a single transposition cipher. The key to the transposition cipher would be a list of the source and destination locations, or just a list of final destinations of the blocks. It's not a very good one because it may well be that you do not swap certain blocks or that you swap something back and forth a few times.
It is not possible for somebody to recover the original file with any kind of certainty. This is not because of the cipher but because a file filled with randoms has no distinguishable information; even if the attacker would guess the key correctly, there is no way for the attacker to verify the result.
It would be easy to guess a few of the blocks right though: just return the ciphertext. The blocks are not shuffled that well, so chances are some of them never changed position; this chance for each block is higher than 1/1000 making the cipher insecure.
For multiple files just containing random information the chances of each file is the same as for a single file. If they were somehow interrelated then the contents would not be random. QED.
(Of course if you'd guess the location of one block right for the first file you'd guess them right for all of them when using the same permutation, but again, no way to verify this.)