I thought I remember hearing many sprinkler heads had lead stoppers or something similar that would melt in the heat of the fire opening up the water flow. Not sure if they still do that.
I don't think they use lead as the fuse but, yes -- in a normal system, each head operates independently. If a fire starts directly under a head, and that one head releases enough water to put out the fire, no other heads will open up. If the fire grows faster than one head can handle, then more heads will open. At some point, however, more heads opening is a bug rather than a feature. I don't know how rack systems are calculated but, for ordinary hazard contents (office buildings, light manufacturing, etc.), the amount of water required is based on four heads operating, and the pipes are sized to carry that much water to the most remote part of the building from where the sprinkler main enters the building.
So, in theory, the system will provide full flow to as many as four heads. If more heads open, the pressure in the system drops and the heads don't throw as much water, or throw it as far. They still discharge water, but eventually if enough heads open there's not much more than a drip coming out of each one.