If I encrypt the same file twice with GPG, using the same key, will I get the same result? or is it using some random/psudeo-random segment to improve security like rsynccrypto?
Generally speaking, no, encrypting the same file with the same key will not produce the same file, for three reasons:
The third point also applies when doing password-based encryption (encryption is done with a password, not with a recipient's public key). Password-based encryption also adds a fourth randomization, which is the salt in the password-to-key transform.
GnuPG encryption is not deterministic and thus will return different output for each run. Encrypting, then decrypting is deterministic of course and will always return the same contents.
GnuPG uses asymmetric encryption, which is slow when encrypting huge amounts of data. For this reason, it uses your private key to encrypt a random block cipher which is again used to encrypt your data.
Each time you're encrypting data, a new random block cipher will be generated, so the encrypted data will look different.
I encrypted the same document twice and calculated the MD5 checksums after each encryption: