No, CRA will not take off HST if it's a small business under $30,000/year.
Airbnb does not collect GST/HST from customers, so it’s up to you to add GST/HST to whatever rate you charge for your space and remit the tax to the government. Airbnb also does not share your information with the CRA – that would be a privacy breach – however, if the CRA gets a court order asking Airbnb for information related to users of their service, that information must be forwarded to the CRA, by law.
Please click here for more information about GST/HST.