Also, I can debunk the idea with a simple thought experiment.
Fact: Rukia did not know Ichigo had latent Shinigami powers.
Fact: Rukia tried to transfer a portion of her powers to Ichigo ignorant of the fact that he possessed latent Shinigami powers of his own, but with the intent of making Ichigo a temporary Shinigami.
Conclusion 1: The process can make anyone an 'effective' Shinigami.
Conclusion 2: In accordance with Conclusion 1, the process is self-contained. It doesn't 'wake up' latent powers, it gives an already existing power to someone else (in a percentile, according to Rukia). If functions independent of any latent spiritual talents.
Final Conclusion: Zangetsu was not technically involved with the blade at all, as the process was self-contained. It would have worked the same way on any human (though the size of the Zanpakuto would obviously change from person to person) regardless of whether or not they had latent Shinigami powers. This means that having latent Shinigami powers would not logically have any effect on the process, nor would the process wake those powers up, because the process works on normal humans, and not everybody has latent Shinigami powers.
Rukia didn't know he had latent powers, but still expected him to spontaneously transform into a Shinigami. That is my evidence that Zangetsu wasn't involved in the process. Because she didn't know about Zangetsu's existence, still expected the transfer to work, and the transfer did work (more or less) exactly like she intended. The only thing that happened differently is that she gave more of her power than she intended, but we know why that happened, and it had nothing to do with Zangetsu's existence (Ichigo's own spiritual energy was so large it messed with her powers, which caused her to make a mistake).
Fact: Rukia did not know Ichigo had latent Shinigami powers.
Fact: Rukia tried to transfer a portion of her powers to Ichigo ignorant of the fact that he possessed latent Shinigami powers of his own, but with the intent of making Ichigo a temporary Shinigami.
Conclusion 1: The process can make anyone an 'effective' Shinigami.
Conclusion 2: In accordance with Conclusion 1, the process is self-contained. It doesn't 'wake up' latent powers, it gives an already existing power to someone else (in a percentile, according to Rukia). If functions independent of any latent spiritual talents.
Final Conclusion: Zangetsu was not technically involved with the blade at all, as the process was self-contained. It would have worked the same way on any human (though the size of the Zanpakuto would obviously change from person to person) regardless of whether or not they had latent Shinigami powers. This means that having latent Shinigami powers would not logically have any effect on the process, nor would the process wake those powers up, because the process works on normal humans, and not everybody has latent Shinigami powers.
Rukia didn't know he had latent powers, but still expected him to spontaneously transform into a Shinigami. That is my evidence that Zangetsu wasn't involved in the process. Because she didn't know about Zangetsu's existence, still expected the transfer to work, and the transfer did work (more or less) exactly like she intended. The only thing that happened differently is that she gave more of her power than she intended, but we know why that happened, and it had nothing to do with Zangetsu's existence (Ichigo's own spiritual energy was so large it messed with her powers, which caused her to make a mistake).
Fact: Exposure to Shinigami power levels above a certain minimum causes dormant spiritual abilities to awaken.
Fact: Ichigo himself had dormant Shinigami abilities.
Fact: Ichigo himself was above the minimum level to activate dormant spiritual abilities.
Conclusion: Being injected with Shinigami abilities 'might possibly' awake dormant Shinigami abilities.
My thought experiment contradicts your second conclusion.