Yes, I think it is. The lates version of the CX rules says:

"Intermediate surface sectors permitted at passenger's expense. Surface sectors are counted as one stopover. When continents are crossed by surface, the stopover may be counted in either continent."

So it IS allowed to take a surface segment between continents.

If you decide to go to Machu Pichu - you should DEFINITELY do the three day hike to get there. You will appreciate it so much more. Porters will carry just about everything for you - and people of all levels of fitness were doing it while I was there. La Paz is a brilliant city, but make sure you go on the prison tour while you are there. Titcaca is well worth a visit, and I recommend you spend a night on one of the islands in Titicaca with a local family ... this can be organised locally.

In Chile, the NAVIMAG ferry from Puerto Natales (nearest is LA city is Punta Arenas) to Puerto Mont is brilliant. It's a RORO freight ferry with passenger accommodation. A fantastic way to see some of the most beautiful scenery in the world.

From Punta Arenas, LA used to fly to the Falkland Islands (MPN). This service is on again and off again - depends on the politics between Chile and UK. Worth it if you can get it.

The "continent" of the Falklands can be debated by airlines. Originally, QF said it was part of Europe ! Eventually they saw the lunacy of this suggestion.