What can you expect from NGO's like the Red Cross

Are you expecting any help from non profit or NGO in an emergency?

For me, no. If some help arrives I'll be grateful for it.

They will get to most places, eventually. As Chaos says, if they show up, great. Be prepared for them not to.

Our predictable local issue is wildfire. The Red Cross has been quick to establish shelters for those evacuated, although most people get a room or stay with friends or family. I am sure their response would be slower in the event of a major earthquake or something similar.

I rely on my own efforts first, since outside help can be delayed for any number of reasons.

It depends on the scale of the emergency. In most emergencies they will provide help fast. The coverage allows for response times of less than 20 minuntes.
In a larger scale emergency they may be slower.
Being prepared for low priority issues is a good idea.

The Red Cross will be setting up shelters that you can go to, but are very limited on their ability to go out and get to you. They rely on volunteers, and not enough of them. You should be prepared to be self sufficient for at least a few days in any case. The unexpected always seems to happen.