Microdermabrasion for Under Eye Bags?

Sorry to say but microdermabrasion is such a superficial process that you are unlikely to see any benefit for the deeper structures.  Go see an expert in your area in peri-orbital rejuvenation.

There are many ways to do microdermabrasion.  The really superficial ones won't really make a difference. There are some physician grade machines that can go deeper with stronger suction.  But you would really need a doctor to do it or some one under the close supervision of a doctor doing it.  Essentially, when you get into the deeper, stronger ones you are doing some resurfacing.  This could help increase a layer of collagen that could help with the bags to a small degree.  Other better options include fillers, fat injections, midface lift, lower blepharoplasty, and lower eyelid rim facial implants.