It would take nation-state level resources for Amazon to even match one of the top 10 mining pools, and they would have to commit those resources to this end for an indefinate period of time. Even the NSA couldn't pull this one off, and they tried it more than a year ago.
They did? Do you have a link? (Not because I don't believe you, but because I'd like to read more about it.)
Search this forum for the elusive "mystery miner" of yesteryear.