I've got no problem with the purely theoretical thought experiment posed here. I think we all agree that, as a practical matter (rather than intellectual self-pleasuring) the patch's effect is, if non-zero, at least utterly insignificant.
There are parallels here with software development, surprising as that may seem, as well as other engineering disciplines. When writing code, how the code is written, compiled, etc. can change the performance of the code. Code writers will often write code, then go back over it and optimize it, trying to squeeze more performance out of it, doing the same computation for less time, energy use, whatever. While any code can, in theory, be optimized, it rarely pays to optimize all code. Rather, profiling tools are used that show where the code is spending most of its time, and then the code that is having the greatest impact on time are optimized first, achieving the best bang for the buck. And, really, the optimization that usually achieves the greatest results occurs during design stages where the basic architecture is conceived; a more efficient architecture programmed without optimization can be way better than a crappy architecture that's then micro-optimized to hell and back.
If the OP were really interested in maximizing his performance, he'd be asking whether he's got the right bike, then the right accessories on the bike, the right tires, the right clothes and helmet, etc. Eventually, way down near the bottom of the list of every conceivable factor that might have a measurable impact on performance, one would find the question of whether a given inner tube was patched or not. This question would probably be just behind whether to shave one's eyebrows, and just ahead of whether or not one should wax the frames of one's sunglasses.