So for the sake of argument, we all know that Jesus was a traveling man, for three years before his execution. Nations didn't have protected borders (some cities did), and Caesar's reach was everywhere Jesus ever went. Thus, for those three years, Jesus was more nomadic than an "immigrant".
But even saying that somehow being nomadic and being an immigrant are on par, what creates a comparison between Jesus Christ and illegal immigrants of today? There is no logical line to be drawn.