Can longer paths consume less fuel than the (shorter) great circle path?
That depends how you define longer in aviation. As you can look at it geographically or on the clock.

The hard answer is no, the most fuel efficient route is the one that has the aircraft in the air for the shortest amount of time. If you can take advantage of a big tail wind 20 miles south of the geographically shortest route or at a slightly higher altitude you may burn a bit of fuel getting there but on long haul flights you can make up for the burn, and even gain quite a bit by taking advantage of the winds 

Similarly headwinds can really kill your efficiency even over short distances.