Those who refuse to enter the country legally are already far less likely to change for the better or contribute to society.
I'm not sure if that's really true. There are many illegals that come here and become productive member of society...others don't. Many enter illegally and then work their way to become legal as well. Again many don't.
The greater point is that we need to create an incentive for legal immigration and not for illegal immigration. Reward the ones that follow process and be tough on those who don't. It's the only way forward.