I have a 2001 Lincoln LS and the Ford dealership is telling me that they can't update my PCM because my mega fuse is blown do a mega fuse have anything to do with the memory

Really depends on which fuse is out. If the PCM has no power it can not be reprogrammed. The issue is what made the fuse break and why does the Dealership think the PCM needs reprogramming? You do not know if the PCM will work until it is powered up unless certain connection points are tested and it shows the PCM is dead. This would be like saying the insides of your PCM are burnt up. If the PCM is burnt up restoring power will not fix it.

Probably a better way to to say it is you need to know if the PCM was burned up and if that is why the fuse broke. The fuse is suppose to protect the PCM before it is damaged. You could smoke another PCM if you connect it up to the car without repairing the problem first.. But the PCM is a computer and the memory can be lost. But like other computers there are Read only programming and programs which can be rewritten. If the circuits are good then the old PCM can be reprogrammed when power is restored.