Sure. You could even do a STUXNET type attack where the pathogen is highly transmissible and perfectly benign to everyone but your target. Release it in a train station in Budapest and wait.
Extremely unlikely. Viruses would lose the gene if it's non-essential, before it got to your target. They're designed to make lots of mistakes in replication to diversify quickly, and without selective pressure, will not retain high fidelity genetic material. Sure, you could mutate the polymerase, but then you have a replication problem as well. How is this virus spread? Particularly without inducing a cough. There's no guarantee of exposure.
Bacteria have more genetic stability but are even harder to spread because most people are already colonized and disruption of that homeostasis is often difficult, and symptomatic.
None of that even addresses how you'd engineer something to be benign to everyone but one person.
