Are most Libertarians for unrestricted immigration provided that welfare is abolished?

Seeing as the only people who would then immigrate to the U.S are productive people who want to work and not live on government handouts, are most libertarians then for unrestricted immigration provided that first all social assistance and government assistance programs are abolished? I mean, once that is done, wouldn't it be considered anti-libtertarian for the government to then interfere with immigration which harms the potential of the free-market?