Given Alcubierre's math, and White's calculations, it's a viable avenue of research to pursue.
Whether or not it is practical as FTL, and given the expected maximum apparent speed of about 10 times the speed of light (White), and that the math says it should be able to be done, an attempt to implement a prototype series should be of immense benefit. Even if the drive fails to work, the drive testing will provide interesting measurements.
Therefore, investigations of Alcubierre's Warp Drive equations in a practical (rather than theoretical) mode are of use scientifically.
Also note: Any measured effect, even if not what is predicted, will lead to improvements in the theory.
Further, NASA is allowing White to pursue a practical experiment.
Note that Warp Drive, even if it doesn't allow for FTL (or as Alcubierre's theory notes, apparent FTL by STL movement of the craft within STL movement of the space the craft is moving through), a STL version will still massively reduce travel times. A 0.01C drive puts Mars a mere few hours away. At furthest distance, Mars is about 18 light minutes away; 1800 minutes travel time is 30 hours - not even 2 days.
Note that, for logistical and health purposes, a roughly 60-90 day mission (round trip) is about the limit. White has implied that he expects 10 C to be practical - this puts Alpha Centauri, home of the nearest detected extrasolar planet, at 156 days travel time. So, for practical purposes, a 10 C drive isn't an interstellar one. At 40 C apparent velocity, the Alpha Centauri system becomes reasonably practical. This means that, unless apparent speeds higher than White's worked 10 C examples are practical, the Warp Drive is going to still be an in-system drive.
It is worth noting that, as of May 2015, NASA thinks the EM-Drive may in fact be generating an Alcubierre warp, and is in fact generating thrust in a vacuum. Dr. White is working on the team testing this drive.
NASA has yet to release any data that this author can find on Dr. White's approved tests of a pure Warp Drive, but if the EM-Drive is generating a warp field, this may be a result of two lines of unrelated research converging.
White, Harold "Sonny", Warp Field Mechanics 101 (http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20110015936_2011016932.pdf) Retrieved 5 August 2013.
Peckham, Matt, NASA Actually Working on Warp Drive (http://techland.time.com/2012/09/19/nasa-actually-working-on-faster-than-light-warp-drive/) Retrieved 5 August 2013.
José Rodal, Ph.D, Jeremiah Mullikin and Noel Munson, Evaluating NASA's Futuristic EM-Drive, (http://www.nasaspaceflight.com/2015/04/evaluating-nasas-futuristic-em-drive/), Retrieved 3 May 2015.