Will Erbium Laser Around Mouth and Undereyes Cause Uneven Pigmentation?

What you describe is done very commonly.  Fraxel Repair can be done on the perioral and periorbital areas while the rest of the face is blended with Fraxel Restore, Fraxel Dual, Chemical peel or other mild resurfacing. Compared to ablative non-fractional carbon dioxide laser resurfacing, there is much less chance of developing hypopigmentation in the segmented areas with the fractional CO2 laser treatment. Erbium, specifically, such as Fraxel Restore, and non fractional erbium can also be done around the eyes and mouth, but in this cirucmstance and Fraxel Repair, it does depend on your coloration and susceptibility to developing post inflammatory hyperpigmentation.

There are several variables to consider, especially your skin color type (Fitzpatrick I-VI)  as well as the depth of the treatment around the eyes and mouth. The more sun damage one has and the darker one's skin is, the more likely that there could be a demarcation line between the deeper and more superficially treated areas. On a positive note,  unlike the occasionally seen complication of hypo-pigmentation with CO2 ablative resurfacing,  undesirable dramatic depigmentation with erbium resurfacing is not generally a concern.  Also, having a micro-peel over the rest of the face at the same session is a good strategy to help with blending.

Whether you will have uneven pigmentation or the extent of uneven pigmentation will depend on the starting point of your skin, the settings utilized, and the skill and technique of the practitioner.