No, I wouldn't recommend it.
Some people think garlic is helpful to the HUMAN immune system, or that is it helpful to humans because compounds in garlic are antibacterial. Bees are biologically very different - remember that they don't even have blood as we usually think of it. So just because garlic might help humans doesn't mean it would help bees. It might even hurt them!
Also, even if garlic worked to help the bees' immune system, that would not help with mites. Mites are a parasite - they bite the bees and suck their body fluids. The bees' immune system cannot stop problems with mites.
I suggest you stick to plain sugar for your dusting.