Maybe, maybe not - you'd have to define which complex set of chemical combination is happiness and which isn't. But why? We know a lot about neurochemistry. We know a lot about receptors, neuromodulators and their interactions (serotonin, addiction). As a biologist I don't understand - why would you want even study something that doesn't exist (happiness), when you can study specific parts of neurochemistry that are more practical and may have actual benefits (like reduction of addiction or help with schizophrenia)