Yes whiskey does kill bacteria in your throat.
Whiskey which contains alcohol kills most bacteria that is in your throat and if you have a sore throat then drinking some whiskey can help kill that bacteria and help get rid of the sore throat.
I've had good results when gargling and even drinking some whiskey when I had a sore throat and it helped the sore throat go away much sooner.
Most bacteria cannot survive being in contact with alcohol so drinking some whiskey or other alcohol can kill the bacteria.
Making a hot toddy when you have a cold using some whiskey and drinking it can also help a cold go away much sooner.
Whenever I have a cold I drink a few hot toddies and the cold gets better sooner than it would without.