I would not say it is.
Happiness is an emotion. Just is regret, sadness, solidarity, grief, etc. In most scenarios happiness is an attributed factor and result of struggle, but not always. Someone could have the worst life imaginable, but just as well be content. Anyone can be truly happy, no matter the situation. This does not mean struggle is dismissed as a factor in the becoming of happiness, however. Many things come from struggles, and happiness is a common emotion once the struggle is over.
This is only eight sentences, but it's a good start.