If I were to harvest an agave plant for its nectar, would it kill the plant? I have watched videos of the process and it seems quite invasive.
When harvesting agave nectar, generally the whole plant is harvested at once to get to the core, where most of the sap is. There isn't exactly an easy way to continually get nectar from the agave plant since it is herbaceous, whereas something like maple trees can be tapped because the wood can support the spigot.
Agave is more closely related to asparagus and hyacinths than to cactus. They are perrenial, you can harvest the lowest half of the leaves to make it look like a little palm tree, it will die after flowering, it takes 10-15 years to flower.