Searle's failure to understand Chinese when he manipulates the symbols in the Chinese room would not refute the theory that thinking is symbol manipulation any more than his failure to see light when he waves a magnet would refute the theory that light is electromagnetic oscillation. One would fail to see it simply because its frequency was below the retinal threshold for visible light. So Searle's argument is correct after all. You are essentially saying that something can be one thing at a low speed, and a qualitatively different thing at fast speed. Such things certainly are possible, not just with respect to time, but with repect to other physical dimensions, such as temperature.
Phase transitions are examples.
It simply points out that, based on the kinds of things we already know and have no reasons to doubt, it is overwhelmingly unlikely that memorizing and executing a bunch of meaningless sguiggle-operation rules will generate either a conscious understanding of Chinese in the mind of Searle, or a second mind in Searle's head, that consciously understands the Chinese while Searle does not. Someone can be really slow, taking minutes, hours, or even years to twig on something. If someone could produce an extremely slow plane that crept along so gradually that it was virtually standing still most of the time, like a helicopter, it would still be flying. So, yes, there is a potential issue about timing, but this image does not quite capture it.