It probably will. The factors that govern antibiotic effectiveness are distribution and sensitivity. If the bacteria in your throat are resistant to the antibiotic and those in your finger are not, then one will be cured and the other won't. Distribution is dependent on the site of infection. Some places in the body, such as the brain, have barrieirs to keep out unwanted substances, and this may keep out the antibiotic and so prevent it from working. Other sites with similar problems can be the urinary tract (too much fluid washing it away) the sinuses (slow blood supply) and the teeth (too much bone).