For preschool kids my view is that schooling does not necessarily inculcate the desirable social behavior ( listening skills,caring for others,making others feel good, handling egos, self control etc).
My son smiles a lot which I feel is right on top of desirable social behavior, he is naturally gifted in engaging with people – initiating play and conversation with others, using please, thanks and sorry appropriately and patiently waiting for his turn. He has fair levels of emotional intelligence – knowing how to pacify, keep others happy and so on, and he has not been schooled till now.
And I have seen kids who despite going to school, lack manners, are bullies and do not know how to treat others. I might be wrong but I have a strong intuition that schooling really does not make a huge difference to the desirable social behavior outcomes, on the contrary,it seems kids going to highly expensive schools are more reserved and unfriendly towards others especially to people who do not belong to their social status and this I have observed across all age groups.
Socially desirable behavior gets linked to selectivity and bias with age,when and with whom and to what extent, one resorts to socially desirable behavior depends totally on the circumstance. The proof is – people reserving even their smiles for the people they approve of, and not bestowing it freely upon others unbiased. The same person who treats a poor person like an animal can be at his best behavior with a rich person. But I do believe that there might be some very good schools who go an extra mile to develop good qualities in kids which bring out socially desirable behavior.But in the end I want to say that if you are a good person and treat your kid with love and respect, he/she will surely have socially desirable behavior.