For the long term survival of humanity? I think so, because it is the only place I believe we can establish a self sustaining colony with only slight advances in current technology because it has all the resources needed in forms similar to Earth. Having that second base will then push technology to the point where we can expand further even to the Oort Cloud. From there we can populate the galaxy in the polynesian mode. This protects us from: Human induced catastophe, supervolcanism, EL impacts, Gamma ray bursts, super plagues, death of the sun etc.

Necessary for economic recovery? NO

Necessary for survival of our civilization until the Earth becomes uninhabitable? Maybe. Depends on how confident you are that we will find new resources to replace the ones we use up without going into space.

There are no sure bets on what will drive people to go to Mars other than that if we don't go and look we won't find any. This is the same issue that's faced humanity since it originated in Africa. I think going and looking has worked out pretty well. The most likely possibilities we know of are deuterium, asteroid access, and biotechnology although all of these are low probability at this point in time depending on unknowns like life on Mars or breakthroughs in technology like CATS or fusion.

Regards,
Mark