It's not clear what precisely you're asking.

"Does world suffering actually cause people to feel sad?" Yes, of course it does. (If it doesn't for you, you're not necessarily a bad person or something, but you have perhaps compartmentalized it better than some people do.)

"Does the sadness people feel from world suffering cause them to take meaningful action?" Yes as well, though it's not as common. Some people who do feel sad about these things aren't necessarily in a position to do anything about it. (For example, I would ask as a counter - how would someone who feels "genuine concern", as you put it, end the suffering in Iran? What actions would you expect to see out of such a person?)