Can Body Fat From Drinking Alcohol Be Exercised Away?

Yes,just like other fat it was deposited on your body from taking in more calories than you were burning.
Alcohol is laden with calories!  That is why the first step on any diet is to eliminate it. So you need to start burning more calories. If you are not used to doing exercise I suggest you
consult a doctor or heath professional first.
Start slowly,eat three meals a day,two healthy snacks like fruit
or nuts,reduce sugar intake and eliminate alcohol.
A trick to burning more calories is to exercise before you eat as you will burn more calories and feel less like eating too much, or drinking for that matter.Then drink two glasses of water before you eat,you will have lost that by sweating.
By the way,gin with light tonic or soda is supposed to be the drink with the lowest calories.
Good luck in reducing your body fat. It can be done