That is absolutely possible.

Many of the people on this forum are, what I like to call, "papier mache traditionalists."  So when someone somes in here and asks a question like this the answer they give is answered from the pulp-and-glue perspective.  But I think if you used some of the more non-traditional techniques you would have better luck.  True 'papier mache' is mashed-up paper (pulp) and glue and is typically molded much like clay.  However, I don't think this is the best technique to make a large cave.  I would suggest making a lumber frame to support the structure.  Then use chicken wire or other wire mesh to create the contours and rock formations around the frame.  Then get some sturdy brown paper (like grocery bags; it needs to be sturdy or you'll begin to see the outline of the wire mesh pattern through the paper) from a office supply store, hardware store, etc... or you can recycle grocery bags.  While you're there, get a few gallons of white glue (the stuff you used in grade school; Elmer's, etc.).  In a bucket, thin the glue with water, almost in half.  Cut the paper into strips, wide strips-6", 12", whatever.  And dip the strips into the glue to soak them.  Pull them out and squeeze out the excess glue.  Lay the paper over the wire mesh frame.  Use the crumples in the paper to your advantage to get really great looking rocks.  Then paint, you can use regular latex paint, same stuff you'd use on your walls at home.  Get some fake ferns and insects and you're all set.