Yes, it is possible. I went to Tamatert - a small berber village about an hour from Marrakesh. We stayed at Douar Samra and had a lovely time. No touts, just a real berber village.
We then went to Essaouira for the Gnaoua festival. I thought there would be wall to wall touts but I was wrong. Essouira is a laid back place. There were people calling out from stalls or displaying wares, but there was not the high pressure, relentless touts that I encountered in other Moroccan cities. We could walk the streets without someone constantly offering to be our guide. I highly recommend both places.