Yes, a donation to most of these non-profits can not be for any specific catastrophe. They collect money for any and all events all over the world. The same goes for red cross & red crescent. On the other hand they say that they dont wait for donations for a specific event and have spent money already from other donors so it all evens out.
According to a study 80 percent of non-profits spend 90 percent of the money on overheads, so 10 percent of the money goes to the cause and 90 percent to administration. This is not true for prominent emergency relief organizations.
Personally I trust the Edhi foundation and usually donate to them.