Can a blocked sinus cause half of face and neck to be numb?

If may: Congestion in one side of sinuses generally cause some degree of swelling and tenderness on that side of face.

Possibly, likely=No;: depends on what you mean, what is actually occurring. The term "sinus" (mucous membrane lined air filled cavities) is widely used for marketing to sell all kinds of products & services to customers who do not understand their anatomy or body physiology. Might sensations from within a maxillary sinus be perceived as half of lower face? Yes, but usually as pain, not numb. Extend to neck? Unlikely.

Suspect not: numbness is a subjective term sometimes. This sinus blockage can cause facial pain and frontal headaches but numbness is unusual . This would need to be worked up and look for another cause. See your doc for further advice.