The slightest change (even by a single bit) you introduce on the input of the hash function will result in generating a completely different output (result) which is completely independent from the previous one. Therefore, there will be no predictable patterns no matter how long the session is.
The only way this can be exploited is if your system generates weak server seeds and the player manages to crack their hashes.

There is nothing wrong in using random nonces (if you believe they are more secure) and it doesn't affect the provably fairness of your games as long as you disclose them (or their hashes) before the game starts and allow the user to edit the client seed after the nonce has been revealed.