Can you play a new player game of Carcassonne w/o farms?
You could do, the game would work perfectly well without farmers.  I would argue against it because this still leaves the new players in a position where they don't see farms being used and don't see how they can score highly if placed well despite the long-term sacrifice of a piece.

In my experience with teaching Carcassonne, players tend to go very quickly from not understanding how they work, to playing too many farmers too early, then getting a good grasp within a few games.  Just be patient.