if you were to fall of a ship in the middle of the sea somewhere and were to find a weather buoy. If you were to climb on it and break it, how long would it take that NOAA comes to save you?

Honestly, you're looking at a really bad situation. Those weather buoys aren't exactly designed for people to hang out on, and if you manage to break one, you're probably just triggering a sensor alert for "equipment malfunction" rather than a distress signal for a human. The maintenance teams aren't exactly on speed dial for a broken sensor, so nobody is going to hop in a boat and rush out there just because a buoy stopped sending data. They might schedule a repair for weeks or even months later, depending on where it is.

If you're stuck out there, your best bet is that the buoy is transmitting its location via satellite. If the system goes dark because you messed it up, you're essentially invisible. NOAA doesn't have a constant live feed of someone watching every buoy to see if a human climbed on it. You'd be better off waving at a passing tanker or hoping you have some other way to call for help, because waiting for a rescue based on a broken piece of equipment is definitely not a survival strategy I'd bet my life on.