Can also be used as noun referring to someone's mouth and at the same time suggesting they suck dick with it. Used primarily to describe someone's mouth who talks too much, is too loud, or says something you don't like (relates more to speech than anything else). I've never heard it used in reference to eating.
I wish that loud bitch over there would shut her dick sucker already.
John: Eat shit and die asshole
Joe: Shut your dick sucker and throw down
Get away from me with that dick sucker -- said as a nappy ho tries to kiss you.
Biff: Eat shit and die asshole
Joe: I'm gonna punch you in your dick sucker you little bitch