Teach him now or teach him later. Your choice mom.
He needs to know that you won't cave to that method of 'communication'. He surely could figure out another way with a little help from you. You've been showing him the ASL... Perhaps you could teach him the signs for "use your words" and then do those signs when he yells at you.
He needs to understand that yelling does NOT get him what he wants. If you know what he wants before he screams, and want to handle it, then do. But if he screams before you do whatever it is, you need to not do what it is... walk away. Tell him that you don't understand screaming and you'll be back when he can quiet down. Obviously, he doesn't have the vocabulary (verbal or sign) to communicate everything he might be trying to... so do what every mommy does... ask him questions. Surely he knows how to nod yes or no.
He sees you put his drink on the counter and starts screaming. You turn to him and say "Mommy can't understand screaming. Do you want me to get something for you? Do you want your drink? " When he nods or says "yes" then sign "please" for him... and have him copy you. Then when you hand him the drink you can show him "thank you".
Don't make it into a battle, but give him the words/signs AS HE NEEDS THEM. Practice makes perfect. :)