Regardless of whether it would improve Junior's approval rating, the supreme law of the land says otherwise.

Once a refugee claimant is in Canada then the Charter is engaged and "fundamental justice" (or version of due process) is required and that has come to mean an oral hearing on the merits of the claim before the Refugee Protection Division per the 1985 SCOC decision in Singh v Canada [1985] 1 S.C.R. 177.  The government exploited a technical loophole in the Singh decision and designated the USA as a Safe Third Country but that only works at the Port of Entry because technically those claimants are not yet IN Canada.

The Harper government recognized this legal fact and that is why they  continued to process claimants who entered Canada illegally or perhaps more accurately irregularly in that s. 133 of the Immigration and Refugee Protection Act exempts refugees from being prosecuted and punished for what would be for other migrants an illegal entry.