How to safely dig a 12 inch diameter hole with an 8 inch auger
You have the general idea, but whether this is successful depends on several things, including soil type, the presence of rocks, and the weight and rigidity of the boring equipment. In any event, expect to get a good upper-body workout. 

I'd bore a hole with a 2" offset, perpendicular to the fence run, then shift the equipment 4" and bore again, creating an oblong bore. You'll still have to clear it by hand as some material will fall back into the original bore cavity. You could try a third bore, but I doubt the equipment will be rigid enough to accomplish much. 

You'll end up with a hole that's tapered to the bottom, but you should be able to get enough concrete around the top to secure the posts.