FDA Deeming Authority Clarification Act of 2017 This bill amends the Federal Food, Drug, and Cosmetic Act (FFDCA) to: (1) revise premarket review and reporting requirements for products newly deemed by the Food and Drug Administration (FDA) to be tobacco products; and (2) grant the FDA the authority to regulate vapor products, which include products that produce vapor with nicotine (e.g., e-cigarettes) and nicotine intended to be used with such a product (e.g., nicotine cartridges). A product is not subject to premarket review by the FDA if it is marketed before it is deemed a tobacco product. The bill delays deadlines for reports to the FDA on products similar to a marketed product that are introduced to market less than 21 months after that type of product is deemed a tobacco product. The bill grants the FDA regulatory authority over vapor products that is in addition to the FDA's existing authority to regulate vapor products as tobacco products. Provisions of the FFDCA applicable to tobacco product components also apply to vapor product batteries. The FDA must establish standards for vapor product batteries. Vapor products first marketed not later than 24 months after enactment of this bill are not subject to premarket review or reporting requirements based on changes to the product's battery to conform to standards. Vapor products may not be advertised in publications, except publications with adult readership. Vapor products may be sold only face-to-face, through vending machines in facilities where only adults are permitted, or by mail order. Vapor products must be labeled with their nicotine content and specified phrases. Retailers of vapor products must register with the FDA.