It really does. Apparently-random data can't be compressed at all, by the pigeonhole principle.

I mean, you could run it through whatever algorithm for fun, but it won't accomplish anything.

Encrypt then sign. Always authenticate before any other operations like decryption. Don't violate the cryptographic doom principle.

Encrypt then sign. Verification is often much faster than (or at worst as fast as) decryption. Signature can also be verified without decryption key, making it possible to verify the data along the way.