The claim of persecution will be against their home country, not the USA.

Whether or not they are Convention Refugees will be determined by the Refugee Protection Division for those eligible to make refugee claims.  If they are not Convention Refugees then Canada is not obligated to offer protection.

I recall the two vessels arriving with Tamil migrants claiming refugee status from Sri Lankan persecution and the same allegations of them being economic migrants was being made.  And the result?  Most of them have been determined to be refugees.

There is a loophole be exploited and the law skirted but it is the government by the  Safe Third Country Agreement exploits a narrow and technical loophole in the law set out in Singh v Canada (Minister of Employment and Immigration), [1985] 1 S.C.R. 177.  That case held "everyone" in Canada has s. 7 Charter rights (and that includes person illegally in Canada.  Technically a person at a Port of Entry is not "in Canada" so back to the USA.