Yes its a good indicator and no there won't be many false positives.
A high-entropy file indicates that a file is either well-encrypted, well-compressed or just contains truly random bytes.
Most compression formats have recognizable headers etc so these can be easily distinguished.
Most people do not have files of random bytes lying around - why would they?
Strong cryptography strives for ciphertext indistinguishability. Which is a necessary property for security, but which also makes it stand out.
So imagine you are the police or border agent interrogating a suspect. There is a file on their computer that is seemingly random. You will conclude that it must be encrypted, and demand the suspect hand over the keys.
People also strive to find "distinguishers" for standard ciphers and encryption formats. For example, trucrypt.
Hiding a message, beyond just encrypting it, is called steganography.