Does that take into account that much of the other 97% of the nation output depends on workers that need the product of that 3% in order to work efficiently?

It doesn't. It treats the economy not as a dependency tree of goods and services but as abstract disjointed numbers that can be considered as independent variables.

So if agricultural output fell by 50% he isn't considering how this would affect the cost of living and it's impact on labor prices and supply, which would cascade towards the whole economy. He's pretending it doesn't matter because the exchange value of that output is proportionately low in GDP calculations.