There's nothing inherent to the Chinese Room thought experiment that prohibits the operator inside from using a random number source combined with an arbitrarily sophisticated sequence of lookup tables to produce "stochastic parrot" behaviour. Anyone who has played as a Dungeon Master in D&D has used dice and tables for this.

Similarly for feedback. All the operator needs to do is log each input in a file marked for that user and then when new input arrives the old input is used as context in the lookup table. Ultimately, arbitrarily sophisticated intelligent behaviour can be produced without the operator ever having any understanding of it.