I definitely don't think it would be quieter with a buddy. More likely you would then have twice the noise. If you are worried he is bored or too lonely then put soft music on in the room or turn a tv in that room to cartoons or animal shows they seem to like the bright colors and funny noises on cartoons or the nature sounds on animal channels. Also you could try getting a birdie mirror for him. Don't leave it in the cage at all times because some will get very protective of their mirror buddy. But if he percieves to have a cage mate at times he may try using quiet chattering to talk to his mirror buddy instead of louder screams. Make sure he has plenty of toys both noise makers, wooden chewing toys and colorful toys.
How long have you had your cockatiel? If not long it could be he is just still settling in, also now it is getting closer to spring and depending on his age many are noisier when hormonal.
You can try to curb the screaming by doing the ignore/reward technique. When in the room with him speak in a quiet voice or whisper many birds will quiet down when they hear everyone else doing the same, if he is quiet reward with praise and even treats. If he is noisy ignore him and go into a different room try to stay out of the room until he quietens then return to the room with praise and treat. He will after a seemingly long period of patience start to notice he is rewarded and has company when quiet and is ignored when loud.
Do you have a schedule sleep time for him with around 12 hours of "dark" "quiet" time? Many birds will not sleep unless it is mainly dark and quiet in the room they are located in and they will become noisier and more aggressive if not getting enough sleep. Do you cover the cage at night? If not you might try this as well.