Doesn't that rely on you being the actual owner of the shares? If your shares only exist in Robinhood's database, I don't think SIPC would apply.
EDIT: After some Googling it appears that SIPC does protect securities that weren't actually purchased due to fraud or mismanagement. IANAL so I don't know if that would apply to this specific situation, but they have protected other non-owners before like in the case of Bernie Madoff.