Yes, generally, and some bottlers use a full shrink sleeve label that extends just above the rim of the closure/cap and continues down to the lower edge of the bottle/container. This gives a completed look to the bottle/container and is a security measure to insure the closure/cap is tamper-proof.
There are many choices in labels, different sizes, types and applications. BSD can provide a number of label suppliers to meet your needs. We can also supply you with co-packers who "Private Label" beverages with your company name and logo.