SOME birds will stop screaming when they are introduced to a flockmate in a separate cage and will in fact start interacting with the other bird through quieter vocalizations. But just be aware that at "social" times two cockatiels will be twice as noisy as one. A cockatiel that is already used to screaming will even with a buddy have one or more times a day when they will start their social screaming. This will usually help the other bird whether usually quiet or loud to also scream. So in fact at least part of the time you are getting twice the noise. All of the cockatiels here have buddies either in cages near them or cages with them. I can honestly say the buddies have no helped the noise level in any way. Some birds will no longer scream the entire day but they will still holler if that is what they are used to. The noisy birds are almost guaranteed to at times get the quieter birds to start screaming.
Now then as to the fact you are not able to spend as much time with the one. Is this always going to be the case? Are you just wanting this to be a "pretty bird" one to look at and not interact with? Adding another bird will not make your bird less likely to bite but if you are not going to be spending much time with it, then a new bird will give it company for while you are away. Also be aware that even though you may later want to cage them together whatever their sex this may not work. We have had some cockatiels that just do not like anyone in their territory and will even pluck the crest feathers off of a cage mate or "buddy" who happens to play on the same playgym. We have to watch these because they can cause actual damage to each other and we then have to keep them separated completely so that they may be able to see the others but not come into any real contact with them.
If you are wanting to be able to handle this cockatiel and play with it then you need to not rush into getting another bird. I realize a month can seem like a long time to a person but it is really not so long. For a bird that has not had real socialization it can take many months even sometimes a year or longer to have a truly trusting bird that you can handle and cuddle. So no in the whole setup a month is not long enough to say your bird will not calm down with patience and proper attention.
Okay I know that two males will get along fine, a male and a female will get along fine (again this does depend on the birds some seem to not get along with either!), but there has been some controversy on whether two females will get along. We have not had problems with two females together but I know others who have. To be on the safe side I would probably suggest getting a male but just don't breed them or offer nesting site possibilities as this can cause more stress and many times more aggresssion in the birds.
