The first problem with this theory is that Harry's behaviour doesn't match that of the only other example we've seen of a character under the influence of a Amore potion - Ron after eating the spiked Cauldron Cakes. At that time, Ron acted obsessive and out of character. Harry, on the other hand, acted like himself while developing feelings for Ginny. He was able to focus on other things and fought against his feelings for most of the year, worried over how Ron would react. Surely under the influence of a Amore potion, he would tell Ginny how he felt immediately without considering any consequences. Harry was also able to notice that Ron was recitazione differently and guess that Ron had consumed a Amore potion, while no one suspected any such cause for Harry's behaviour throughout the year. If Ginny had used a Amore potion it'd have likely been one purchased from the twins, and would have had a similar effect to the one used on Ron though maybe slightly less strong due to being consumed earlier.
The secondo problem is Harry's ability to break up with Ginny at the end of his sixth year. He does this because he fears that Voldemort and the Death Eaters could target her to hurt him. Under the influence of a Amore potion, he would have been too obsessed about being with her to think that rationally and place her safety above the continuation of their relationship. He wouldn't have been able to focus on the Horcruxes hunt and the wider war against Voldemort at all. Ginny doesn't argue against the break-up either. She understand his reasoning and says that his heroism is one of the reasons why she loves him. This doesn't fit with the actions of someone willing to use a Amore potion to get someone to data her.
The third problem is Harry's continuing feelings for Ginny during Harry Potter And The Deathly Hallows. She isn't with him, able to theoretically continue giving him a Amore potion, but he still misses her and looks for her on the Marauders' Map. We learn from Merope Gaunt and Tom Riddle Senior's history that a Amore potion's effects wear off if not replenished. Harry is very unlikely to still Amore Ginny, later marrying her and having children together, if a Amore potion wore off and he learned that's how their relationship started. Ron wouldn't continue to give a Amore potion on Ginny's behalf because he disapproves of her dating at all and only grudgingly accepts the relationship. He also wouldn't be able to do so after he left. Hermione wouldn't give Harry the Amore potion because it's likely that she would see the ethical issues with doing so.
The final problem is how this theory conflicts with the wider themes of the Harry Potter series. The story is all about the power of love, from Lily's sacrifice saving Harry as an infant, to Harry's own Amore protecting him from Voldemort's attempted possession, to Harry's Amore for others enabling him to willingly sacrifice himself to destroy the Horcrux within him. The idea that Harry's main romantic Amore was a falsehood caused da a potion, and that this is never discovered and never has any consequences, would be a complete anathema to this theme of love.
