Back to your original question: No, synchronization of the carbs cannot affect or change the timing.
However, timing could affect and change the synchronization. This would be because each pair of cylinders has a different set of points (1&4 and another for 2&3). If they are set to fire at different degrees than each other, then a synchronization of the carbs would likely be disturbed. If you synched them with one setting and then had the timing of one of the points altered, then the original synch would be off. That is why you get the timing correct BEFORE doing a carb synch, and also first get the tappets set properly as that can also alter a synchronization of the carbs.