Yes, there could be disavantages, as sometimes there are Neurons not expressing NeuN in some pathologies, and the lack of expression does not always mean that the neuron is going to die. Check this paper for more info:

http://www.ncbi.nlm.nih.gov/pubmed/15223381

We have also reported something in the same direction:

https://www.researchgate.net/publication/229552162_Effect_of_intracortical_vascular_endothelial_growth_factor_infusion_and_blockade_during_the_critical_period_in_the_rat_visual_cortex

Article Effect of intracortical vascular endothelial growth factor i...

But we also use NeuN to stereologically count cells at all our areas of interest (including cortex and all hippocampal regions).