Yes, the definition of "aesthetics" and "cosmetology" contained in A.R.S §32-501(2)(a) & (6)(b) include the following practice if they are performed for cosmetic purposes:
"Massaging, cleansing, stimulating, manipulating, exercising, beautifying or applying oils, creams, antiseptics, clays, lotions or other preparations, either by hand or by mechanical or electrical appliances."
In addition, the definition of "cosmetology" found in A.R.S. §32-501(6)(c) includes:
"Styling, arranging, dressing, curling, waving, permanent waving, straightening, cleansing, singeing, bleaching, dyeing, tinting, coloring or similarly treated hair."
Eyelash extensions are applied for "cosmetic purposes" as defined in A.R.S §32-502(4) as "for the purpose of beautifying, preserving or conferring comeliness, excluding therapeutic massage and manipulations."