From my understanding (for which I haven't yet perused OP's linked article, so may be off from the current expectations) Warp Drive wouldn't be too brilliant for getting
off planet, or even generally through an atmosphere, but it might well aid actual space travel and (taken to a high-enough art) either mitigate relativistic effects (when they start to be inconvenient) or even 'cheat' the universe into giving us FTL, pretty much as that old Wagon Train In Space series had us believe it might... But with practicality at the lower levels, even, still being theoretical and that old exotic matter problem (as already mentioned) may be the sticking point.
Hmmm... I wonder if we
do get Warp Drive devices zipping around in Earth orbit (and even out into the solar system), whether their passage could be detected by
LIGO, or similar? I suppose it depends on what ripple effects 'leak' from the drive's sphere (or 'lozenge') of influence... But that effective energy dispersion would mean inefficiencies, to my mind, so perhaps sewing it up tight (at the boundaries of the required effect) ought to be the aim of whatever mystical warp technology they'd be employing.
(Or.... there's also the possibility of existing 'gravity gradients' across compressed/expanded space giving a localised effect on the gradient
beyond the travelling device, detectable as a difference from the unperturbed 'background' gravity, at least within a short enough distance on the opposite side of the hypothetical spacecraft to be effectively within the 'umbra' of the gravity-effect 'shadow' concerned... Hmmm....)