Yes, the entire file would be encrypted but with the private key after adding, say, 2048 bits of all 0's to the beginning of the file. After decrypting the whole file, check if the first 2048 bits are all 0's. If they are, good, boot. It can be brute forced, but with 1 in 2^2048 probability of guessing right.

The chain is only as strong as it's weakest link.