Well, yes, theoretically this is possible. We all have certain bacteria on our hands that are always there--they're called resident flora. Now, it is not possible to kill every single bacteria that is on your skin, and this is ok. Our resident bacteria doesn't usually harm us. When we use sanitizer, a majority of the bacteria is destroyed, and only the hardiest, strongest remain. Theoretically these "super" bacteria can multiply so that the entire colony of resident bacteria on your hands is resistant to alcohol....obviously this happens over a period of time and not immediately after using sanitizer just once. When you wash your hands with regular soap (not antibacterial) you're simply removing the bacteria, not killing them, and thus not creating a situation for super bacteria to flourish.
On the other hand, this isn't true for viruses. Viruses are unable to replicate themselves outside the body (bacteria can), so once they're "dead", that's it--there aren't hardier viruses that are left to repopulate your hands b/c viruses simply aren't capable of doing this. A vast majority of stomach illnesses are caused by viruses, and when bacteria is the culprit it is usually introduced to the gut via contaminated food.
I hope this helps some.
nikki