No, remember the application is in two parts- application for sponsorship and application for PR. The sponsorship part is processed only in Canada, and involves only you and your details on the form. The second part, application for PR is processed outside Canada and only concerns the person being sponsored, which is your spouse. If you immigrated to Canada, then a background check would have been done before you even got to Canada in the first place. If you were a Citizenship by birth, then under the Charter of Rights, they cannot immigration cannot investigate you, only the RCMP can, but has to be on a serious matter and not for an immigration cause. Hope this helps.