Performing PCR on samples whose DNA concentration is nul
Nope, you could get amplification from samples that are orders of magnitude below the nanodrop detection limit (~2 ng/uL). To compare: most manuals for polymerases recommend 1 ng of plasmid template, and will probably work with much less, especially if you use a few more cycles.  

But if you expected to see something on the nanodrop, and you get nothing, something else might be completely wrong.