Sure.
The problem is that the brain is not a squishy uniform cell mess that just reacts to some chemicals (dopamine/serotonine/...). All of those are neurotransmitters to specific classes of neurons that have a very specific topological position to perform their function.
So if you just throwing in random neurons here and there, they won't do anything. They are not contributing to any pathways.
Serotonin re-uptake inhibitors and dopamine generator drugs (aka opioids) make the signal send by the "correct" neurons that are there stronger, contributing to the desired effect.
The problem with Alzheimers is the death of "correct" neurons, that occurs before Alzheimer is manifested. So just injecting new ones is unlikely to do anything.
Moreover, the neurons don't just live outside brain. They need to be immortalized to live in a Petri dish. And to acheive it, the only way we can go now is to add factors that in the context of human organism are considered as cancerous.
So it's a combo of "unlikely to be efficient" and "potentially likely to lead to cancer". With Parkinson the tradeoff might be acceptable, but this kind of projects is definitely that raises some red flags for me.
