Welcome to FT traciemarie

There seems to be no hard and fast answer to your question. Is it an AA/LAN booking? In theory yes, they should be able to check your bags through to your destination. In practice some of us (myself included) have found that it cannot or will not be done.

The more segments the less likely in my experience. You may also want to post a question in the Argentina forum too because if Argentina is the same as Chile, Perú and Colombia, you will need to clear customs in EZE so whether or not you can have your bags checked through to USH is potentially academic.