With proper preparation, yes. To reuse my example: it doesn't take long to register an Amazon account, offer a high-paying HIT with a binary download which opens up a port on the computer, and within minutes multiple people across the world will have run your trojan (well-paying HITs go very fast & Turkers are geographically diverse, especially if the requester doesn't set requirements on country*); and then one can begin doing all sorts of other things like fuzzing, SMT solvers to automatically extract vulnerabilities from released patches, building botnets, writing flashworms, etc.

Thanks. Looks like my perception is mainly based on my lack of expertise about security and the resulting inferential distance.

Hard to see how any plausible AI could copy its entire source code & memories over the existing Internet that fast unless it was for some reason already sitting on something like a gigabit link.

Are there good reasons to assume that the first such AI won't be running on a state of the art supercomputer? Take the movie Avatar. The resources needed to render it were: 4,000 Hewlett-Packard servers with 35,000 processor cores with 104 terabytes of RAM and three petabytes of storage. I suppose that it would have been relatively hard to render it on illegally obtained storage and computational resources?

Do we have any estimates on how quickly a superhuman AI's storage requirements would grow? CERN produces 30 petabytes of data per year. If an AI undergoing an intelligence explosion requires to store vast amounts of data then it will be much harder for it to copy itself.

The uncertainties involved here still seem to be too big to claim that a superhuman intelligence will be everywhere moments after you connect it to the Internet.