Does Alarplasty Leave Scars for Life?

Yes, the scars are permanent but if done properly very well hidden. I am giving you link to the photos of one of my patients, Its the woman on the bottom, she had alarplasty as part of the rhinoplasty and you cannot see the scars. I can even send you close up photos of the alar area if you wish.
Regards

As a trusted plastic surgeon, I know that one of the most important aspects of my job is to make the patient’s new, improved appearance look as natural as possible. Scarring can greatly distract from the overall appeal of a nose job, and can make a patient feel self-conscious when they should be feeling confident and excited to show off their new look. Scarring does technically “last forever.” Still, a good surgeon knows exactly where to make the incisions of an alarplasty procedure, hiding the openings in the creases of skin and at distinct angles. In this way, any markings will be well hidden and not really visible to the naked, untrained eye. For a more accurate assessment of how your new nose and any residual scarring will likely heal, ask your surgeon to see before-and-after photos of his or her past patients. 

Nostril reduction surgery (called Alarplasty / Alar Base Reduction) is a procedure that can narrow the width of the nostril base, decrease the amount of nostril flaring, or decrease the size of the nostrils.
It is possible to perform this procedure alone or as part of a rhinoplasty. To accomplish narrowing of the nostril base and nostril flaring, an alar base resection is performed by removing a crescent shape wedge of tissue from the nostril wall.
The incisions are placed in the crease where the nostril wall meets the cheek. When performed correctly, the scar is hidden in the "new" crease where the nostril meets the cheek. The incisions can remain red for several weeks, but generally heal very well and are not noticable after that time.