LAN Argentina will not do any paper work for you.
If you don't get the Argentinian License (Comercial de Primera or ATPL) from ANAC, DSM will not take your application under consideration.
All the conversion process from your FAA License to Argentinian ones is under your own.
So it takes time and money, so If I were you I would visit the ANAC in Buenos Aires inquiring for the conversion process which is not so easier or shorter than in US.
You have also to take the course and the exam for the Radioperator license.
You should count in not less than 6 month to 1 year to have all the process done.
About having the B767 type rating in my opinion is a waste of money because everybody join LAN Argentina through the Baby Bus A320.
There are only 2 B767 and 12 A320... so many people is ahead of any newbie waiting their opportunity to fly the 76.