Something tells me I shouldn't get involved in this argument, but all this back-and-forth is starting to grate on me a little bit.
Here is the issue. Yes, to say that Amourshipping is the entirety of Serena's character is false, because there is, of course, a lot more to her character than just her crush—just as there is more to Ash's character than his impulsiveness, or there is more to Clemont's character than his love for inventing. Serena is not a one-dimensional character with one defined character trait.
However, if one were to say that Amourshipping overshadows Serena's other character traits, then that could be an opinion—a subjective statement—and thus cannot be proven true or false. (Not every opinion/subjective statement has to start with "In my opinion.") Why? Because it depends on the reasoning behind that opinion.
If one were to base that opinion on how the fanbase treats Serena, then yes, Amourshipping does seem to overshadow her other character traits; it does feel like the fanbase emphasizes Amourshipping at the expense of Serena's other character traits. When fans talk about Serena, isn't her crush on Ash often at the forefront of the conversation? In that sense, Amourshipping does overshadow Serena's other character traits, because the fanbase makes it that way.
Within the anime itself, on the other hand, Serena's crush was not given any more attention than her other character traits. In fact, as the series went on and Serena's character began to develop and she focused more on her goal, one could argue her crush was given less attention than her other character traits. If Amourshipping overshadows Serena's other character traits, then that's the fault of the fanbase.