Yes, there is often a mountain of cardboard there. It may or may not be picked up from time to time by the local recycle company, a mom and pop business out of Agua Caliente.
When I was actively involved in recycling here I was amazed at how much cardboard is produced just in this little town!! Imagine what's happening worldwide? In many cases there are alternatives to this packing material, including NO packaging, which would help a lot. Maybe in the future hemp will play a bigger role and more of our beautiful trees can be spared chipping up to make cardboard.
As Brandon notes, cardboard is a useful material for composting, and for sheet mulching - a technique that builds soil and suppresses weeds.
What we can do as individual consumers is to first reduce our consumption, then chose products with less or no packaging, and buy in bulk with reusable containers whenever possible. We now have a wonderful store, La Semilla, that offers many products in bulk, with more added as they become available.