No. GPG doesn't use the public key to do the actual encryption, it generates an intermediate key, uses that to encrypt the message and encrypts that intermediate key with your public key.
Maybe this is too far-fetched and it's beyond what is technically possible today, but wouldn't the decrypted message be the plaintext for the session key and wouldn't then the session key basically be the plaintext for the public key? I suppose it's considered unbreakable because you only get one plaintext per session key?
That I guess would depend on the algo for the PGP key in question. The default these days is RSA 2048 for gpg, which as far as I know is not vulnerable to known plaintext attacks.
The trouble is, if you use the same key to encrypt the same plaintext, you'll get the same ciphertext. Then an eavesdropper can compare the ciphertext you sent her with the ciphertext you sent someone else and see if they are the same.
This is why all worthwhile encryption schemes are nondeterministic, incorporating randomness. If you encrypt the same data twice with GPG, the results will not be the same.