Yes GPG should add appropriate padding (random initialization vector) to not reveal whether two ciphertexts have the same plaintext. It makes no real attempt to conceal that the two plaintexts have the same length. If you want that, best bet is to make all ciphertexts the same length, by padding plaintexts out to 1MB or whatever, and turning off compression. Actually you might first check the manual to see if there is already an option for that. There are a lot, and I no longer keep track.
Cryptographer's saying (Silvio Micali, I think): "A good disguise does not reveal the person's height". So you are on the right track.