A dermaroller greatly enhances the penetration of any skin care products so yes, it is a good idea. The best size for penetration enhancement in that area is a 0.2 mm dermaroller.
The circles under the eyes can have several reasons. The 3 most common ones are:
1) Increased pigmentation of the skin (brown colored dark circles), being quite common in darker skinned individuals. Or melasma, or sunspots.
2) Skin thinning. The underlying tissue such as veins and the orbicularis oculi muscle shine through as bluish, reddish or purplish tones. In addition, because there is not much fat between the skin and the muscle, the dark muscle absorbs the light and that makes the area darker.
3) Loss of fat in the area below the eye, making the area hollow and shadowy.
4) Shadows created by lax tissues, bags under the eyes etc.
I will give you some suggestions to ameliorate the causes mentioned above:
1) Bleaching creams such as hydroquinone or mild acid peels. Do not use Tri Luma since it contains a steroid and that might thin the skin even further. Tretinoin cream. Fillers.
2) The skin can be thickened by a dermaroller and the skin laxity improved. Using Retinoids may help thicken the skin as well. Using fillers such as Restylan or fat grafting will help. Make up concealers help.
3) Fillers such as Restylane or grafting your own fat tissue. This area is very tricky to use fillers on so choose your doctor carefully.
4) Plastic Surgery and/or fillers.
How to roll around the eyes. Please read my answer #2:
https://http://forums.owndoc.com/dermarolling-microneedling/can-i-use-a-dermaroller-on-this-area-under-the-eye-(pic-included)/