Usually, yes. Travel insurance treats altitude sickness like any other illness that comes on during your trip, so the medical part of a plan generally covers treatment.
Three details decide how much help you get.
How high and what you were doing. Many plans exclude trekking or climbing above a set elevation unless you add an adventure upgrade. A tour to high geysers in the Atacama is different from a mountaineering trip, and the plan will treat them differently. Our page on trip coverage for Chile has more on that part of the world.
Getting you down. The cure for serious altitude sickness is lower ground, and sometimes that means an evacuation. Check that the plan includes emergency evacuation and look at the limit.
Cutting the trip short. If a doctor says you need to descend or go home, trip interruption can pay back what you didn’t get to use. Deciding on your own that you feel rough usually isn’t enough.
If Colorado is the high place you’re headed, we wrote a longer piece on altitude sickness in Colorado.