Originally Answered: Antibiotics Resistance?
This is a very good question. The answer to this is not easy to answer in a short paragraph.
First off, Antibiotic resistance is NOT the result of over prescribing antibiotics in the cummunity only, although it is a large portion of it. In general, antibiotic resistance is the result of the overuse and misuse of antibiotics in humans as well as animals. There has been a lot of scrutiny placed on the use of antibiotics in production animals. This is a good topic for another question and I won't get into it here.
Now lets get to your example. Individuals with a prinary viral infection can be susceptible to a secondary bacterial infection where normally the bacterium wouldn't cause an infection on its own. The individual's immune system is weakened due to the viral infection, thereby unable to fight off the bacterial infection. A good example of this can be seen in poutlry. E. coli is the most common cause of bacterial infections in production poultry, but is normally a secondary infection after the birds are first infected with a virus.
Now to get to your question. Giving antibiotics to someone with a viral infection would help prevent a secondary bacterial infection. But the problem is that, as you pointed out, this is a potential infection isn't currently seen. As I am sure you know, antibotic resistance is the result of overuse and misuse of antibiotics. So while giving an antibiotic to an individual may or may not be beneficial to the individual, the continued use of this pratice will lead to more resistant bacteria (which has and is already happening). So, although you may (big if involved there) be helping the individual short term, in the long run you are hurting the population.
Again, this is just a small example. There is no way we could get into the ins and outs of this topic here. A good book to read on the subject is The Antibiotic Paradox by Stuart Levy.