This is their immigration platform in 2004, it is longer than a yes or no answer.
2004 Libertarian party Platform:
Immigration
The Issue: We welcome all refugees to our country and condemn the efforts of U.S. officials to create a new “Berlin Wall” which would keep them captive. We condemn the U.S. government’s policy of barring those refugees from our country and preventing Americans from assisting their passage to help them escape tyranny or improve their economic prospects.
The Principle: We hold that human rights should not be denied or abridged on the basis of nationality. Undocumented non-citizens should not be denied the fundamental freedom to labor and to move about unmolested. Furthermore, immigration must not be restricted for reasons of race, religion, political creed, age or sexual preference. We oppose government welfare and resettlement payments to non-citizens just as we oppose government welfare payments to all other persons.
Solutions: We condemn massive roundups of Hispanic Americans and others by the federal government in its hunt for individuals not possessing required government documents. We strongly oppose all measures that punish employers who hire undocumented workers. Such measures repress free enterprise, harass workers, and systematically discourage employers from hiring Hispanics.
Transitional Action: We call for the elimination of all restrictions on immigration, the abolition of the Immigration and Naturalization Service and the Border Patrol, and a declaration of full amnesty for all people who have entered the country illegally.