I think that yeah once Harry got in school he would have had to been able to get to know Sirius, and I would hope that even though Dumbledore wouldn't have let him live with Sirius, he would at least have the knowledge that he had a godfather and then he could use that against the Dursleys. He might have been better taken care of that way. They might have feared upsetting a full grown wizard.
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Laura//Hufflepuff