How many people would think to first check the Red Cross website first
To be honest, I would have expected the Red Cross to have more important things to do and I wouldn't want to bother them.
Then again, I would have thought people in a disaster would have more important things to do than to go on Facebook.
The Red Cross is a big organisation. They probably have their own IT department, which is located somewhere in Europe or the US, or maybe even in India, but not on the location of the disaster. IT is essential to an organization like the RC, for themselves, but also for victims.
One essential part of recovery from a disaster is stress release. If you know what happened to your family, that saves you from a lot of stress, the stress of uncertainty, even in the case that they are dead. If they are alive, you can contact them, and that helps them recover more easily. Social contact is essential.
Facebook and Google could put a link to the RC website on top of their page for all people who login from Nepal, but better they should use their own site and create an API to the RC database, and sync data.