I need to know something about Turtleneck & Chain.

I want to have a turtleneck, chain, and (fake) light beer for a joke, but my parents are convinced that the 'Turtleneck' in turtleneck & chain means... y'know. The other meaning of turtleneck. Was this the intent of Andy Samberg & co., or does it just come off this way to annoying adults?