Since the code is literally the answer to What comes next after this prompt the answer is yes. Unfortunately there is also a hidden random seed in the engine (which this doesn't seem to address). But if you capture the seed, the exact version of the software and the prompt, the system is completely deterministic.

However there is an unpleasant reality: the system could be incredibly brittle, with the slightest change in input or seed resulting in significantly different output. It would be nice if all small and seemingly inconsequential input perturbations resulted in a cluster of outputs that are more or less the same, but that seems very model dependent.